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CGPA Calculation for Engineering Students: All of us have heard the term CGPA many times in our life and have wondered what it meant. Nowadays, most engineering colleges follow the CGPA system as it is a globally recognized system as it assists a person in understanding where they stand in comparison to their classmates.

Many colleges nowadays demand that students produce their cumulative averages during the entrance process. Here, we have a guide on how to calculate CGPA in engineering if you want to get admitted to one of the engineering branches.

• Advantages of CGPA
• How to Calculate Overall CGPA in Engineering?
• How is CGPA Calculated in India?
• How to Calculate CGPA from SGPA?
• How to Calculate CGPA from SGPA?
• How do the Engineering Colleges Abroad Award/ Calculate CGPA / GPA?
• How do the Indian Engineering Colleges Calculate CGPA?
• What are the disadvantages of using the CGPA or Cumulative Grade Point Average system?
• What is the difference between CGPA and GPA?
• What is the difference between CGPA and SGPA?

What is CGPA?

CGPA refers to ‘Cumulative Grade Point Average.’ It is used to denote a student’s total average performance throughout their academic programs. CGPA is accepted in a high school, Bachelor’s Degree and also in Master’s Degree programs.

The CGPA system is one of the most common evaluation ways, even though the criteria might vary from one country to another. So, it is essential to understand how to calculate CGPA in engineering. CGPA is the total of all your credit points.

Advantages of CGPA

There are various benefits of calculating CGPA, so you should be aware of how to calculate CGPA in engineering. Here are some of the benefits of having the CGPA system of evaluating and grading your results:

• The pressure of marks reduced: The grading standard of education has decreased students’ scoring pressure, which in turn makes them learn without any pressure.
• Identification of Strengths and Weakness: The grading standard of education helps students identify their strengths and weaknesses.
• Grading Pattern is advanced: The grading standard of education is based on a progressive marking pattern.
• Studies become simpler: The grading standard of education has made education more straightforward and more accessible in various ways.
• It also helps the colleges and universities accurately analyze where one stands in comparison to the other students.

How to Calculate CGPA in Engineering?

To calculate CGPA, the students also need to know about the GPA- Grade Point Average. The value represents the average value of the accumulated final grades scored in courses over time. This means that all of your grades are combined altogether, and then they are divided by the total subjects you had in that semester. Engineering students can also convert CPI to a percentage, CGPA to a percentage, and CGPA to marks to get clarity.

CGPA = total of GPA in all semesters/ Total Number of Credit Hour

If you are thinking about how much CGPA you should score to be considered as good CGPA in engineering, the CGPA of 8 or above is usually considered the best. As the competition for studying abroad can be extreme, one should aim for a slightly higher CGPA.

Also, Read:

• Convert CGPA to Percentage
• Converting Percentage to GPA out of 10

How is CGPA Calculated in India?

As the CGPA grading system varies from one country to another, the Indian grading system that is CGPA to percentage conversion differs from other countries and varies from one university to another. Here, we have laid out the general way to calculate CGPA in Engineering or any other courses in India:

CGPA = Percentage/9.5

For instance, the total marks you score in a total of five subjects in a particular semester add up to 250.

How TO Calculate CGPA in University

Step 1: At first, you need to calculate the total percentage you got, that is,

250/500 = 50%

Step 2: Then, you need to calculate the CGPA from percentage; you need to divide your percentage by 9.5 that is,

50/9.5= 5.26 CGPA approximately.

How to Calculate SGPA?

A student’s performance in a semester is indicated by a number called the Semester Grade Point Average or SGPA. The SGPA is a weighted average of the grade points obtained in all the courses, projects, and seminars registered by the student. It can be calculated by simply adding up all the credit points allocated for the subjects and dividing it by the total credits awarded to that semester.

For instance, in a total of 4 subjects, one scored the following grade points:

Subject 1: 9

Subject 2: 6

Subject 3: 8

Subject 4: 7

Let’s say that the total credit for each subject is 10.

Step 1: At first, we will multiply the grade point with the total credit point for each subject:

Subject 1: 9 * 10 = 90

Subject 2: 6 * 10 = 60

Subject 3: 8 * 10 = 80

Subject 4: 7 * 10 = 70

Step 2: To calculate SGPA here, you need to get the total of all the grade points and then divide it by the total credits, that is,

Total grade points: 310

Total credits: 40

To get SGPA, divide the grade points by total credits,

= 310 / 40

= 7.75 SGPA

How to Calculate CGPA from SGPA?

After the universities release the results in the form of CGPA, one still has to convert that CGPA to a percentage if you want to pursue your further studies in a foreign country, as there shall be the requirement for the scores to be in percentage.

Because of this reason, we have given out the pathway of transforming your CGPA to a percentage:

• At first, you need to find the SGPA of all the semesters.
• Once you have the SGPA of all the semesters, add them.
• Divide the addition of the SGPAs by the Number of the semester you have given.
• The Number you get is your CGPA.

For instance, the SGPA of a student for six semesters is,

1. Semester I: 8.0
2. Semester II: 7.0
3. Semester III: 7.4
4. Semester IV: 6.8
5. Semester V: 7.8
6. Semester VI: 7.2

Add all of the SGPA, i.e.,

8.0 + 7.0 + 7.4 + 6.8 + 7.8 + 7.2 = 44.2

Divide the addition by the Number of semesters, i.e.,

44.2 / 6 = 7.37 (CGPA).

How do the Engineering Colleges Abroad Award/ Calculate CGPA / GPA?

Generally, to calculate the SGPA, candidates have to multiply by 10. On the other side, CGPA is calculated with the assistance of credit points. Let us understand how to evaluate CGPA in engineering with the support of an example.

Example: The following scorecard represents the credits and grades scored by a student in a semester. Let us be aware of the process of calculating CGPA in a specific semester.

Subjects	Grade	Credits
Subject 1	A	2
Subject 2	B	2
Subject 3	B	4
Subject 4	B	4
Subject 5	B	4
Subject 6	B	5
Subject 7	A	3
Subject 8	S	4

Average Overall grade: 8.04

Where the grading scale is,

S: 10, A : 8.5, B : 7.5, C : 6.5, D : 5.5, E : 4.5

For each subject, the students are awarded credit and a grade. We multiply the credits with the grades’ allocated score points and divide the result by the total number of credits to get the SGPA. In this case, SGPA is, = 8.04

Now coming on to how to calculate CGPA, it is nothing but the average of all the SGPAs. You can add the SGPA earned in each semester and divide them by the total number of semesters. CGPA can either be calculated out 4 or 10, depending on the university. Let’s say that a person gets the following SGPAs in 6 semesters:

Semesters	SGPA
I	7
II	8
III	9
IV	8
V	6
VI	5

In this case, the CGPA for the course be: = 7.17

One should also note that CGPA can be obtained out of 4 or 10 depending upon the educational university system. Out of 10 can be altered to out of 4 by efficiently dividing the subtotal by ten and multiplying it by 4.

One can also calculate their CGPAs or percentage by calculating the Percentage CGPA calculator for engineering for which you need to know your CGPA (for percentage) or percentage (for CGPA).

How do the Indian Engineering Colleges Calculate CGPA?

There are two ways used when we talk about the evaluation system that is used in India, namely the Relative and Absolute Grading System. Although the latter is the total percentage obtained irrespective of how many students score the same marks, the former highlights the student’s performance compared to others. We have given an example to help you understand how to calculate CGPA in engineering through the relative grading system.

Let’s say that the marks out of 100 are allocated to a certain bracket of grades and numeric values. These are put in a table form below:

Grades	Numeric Value
A+	10
A	9
B	8
C	7
D	6
E	5
F	0

Like we already stated, SGPA is first evaluated, and then the final CGPA is calculated. Following this logic, if we consider that chemistry and maths are awarded a total of 4 credit points each by your university. Thus, the marks and the grade point as per the table given award will be:

90-100 is a ten that is an A+

80-89 is a nine that is an A

70-79 is an eight that is a B

And so on.

So, if someone scores 78 in their chemistry and 98 in their maths, they will get an eight and a 10 for chemistry and maths, respectively. Their CGPA will be:

(The credit allotted to the subject * the point received) / The total credit points

=  =  =  = 9

The final step in calculating CGPA in Engineering can be done through a statistical method. Let us consider that there is X number of students in a class. Students’ means can be denoted by Y and Z and can be known as the standard deviation. Then,

Lower Range of Scores	GRADES	Upper Range of Scores
–	A+	> (Y + 1.5 Z)
(Y + 1.0 Z) <	A	Less than equal to (Y + 1.5 Z)
(Y + 0.5 Z) <	B+	Less than equal to (Y + 1.0 Z)
Y	B	Less than equal to (Y + 0.5 Z)
(Y – 0.5 Z) <	C+	Less than equal to Y
(Y – 1.0 Z) <	C	Less than equal to (Y – 0.5 Z)
(Y – 1.5 Z) <	D	Less than equal to (Y – 1.0 Z)
–	F	Less than equal to (Y – 1.5 Z)

FAQ’s on CGPA Calculation For Engineering Students

Question 1.
What are the disadvantages of using the CGPA or Cumulative Grade Point Average System?

Answer:
Some of the disadvantages of using the CGPA system are given below:

• Demotivation: The CGPA system of education sometimes demotivates the students who can achieve higher.
• Result accuracy: The CGPA system is found deficient in showing the accurate results of students.
• Increase in laziness: A CGPA in the education system has separated the marks among various tasks like presentations, assignments, and final examinations; there is an increase in lethargy due to students’ laziness.
• Performance decreased: Due to the CGPA system of education, students are likely to perform less.

Question 2.
What is the difference between CGPA and GPA?

Answer:
CGPA and GPA are both the calculation of the performance of a person in a course. But the main difference between CGPA and GPA is that CGPA measures the performance throughout the course, including all semesters and units. In contrast, GPA measures the performance of a single semester or unit.

Question 3.
What is the difference between CGPA and SGPA?

Answer:
Cumulative Grade Point Average (CGPA) is used to measure the overall student’s academic performance in schools and universities, and it is for a more extended period. Semester Grade Points Average (SGPA) is an average grade point calculated at the end of an academic session, such as a semester at college, and it is for a shorter period.

Although we have provided you with every necessary information about calculating CGPA in engineering, we realize that the entrance process can get confusing and tiring. We can help you make the perfect application for your dream college, including your CGPA and SOP and essays, as we know that you would not want to risk any aspect of the entrance procedure.

Make use of this simple and straightforward calculator that offers the eigenvalues for a matrix. Eigenvalue Calculator takes the numbers i.e matrix in the input fields and generates the output in less amount of time by hitting the calculate button provided beside the input box.

Eigenvalue Calculator: Are you struggling to get the eigenvalues for matrix? Then, try this handy calculator tool and make your mathematical calculations immediately and easily. This calculator gives the detailed process of obtaining a solution to your question and the direct answer within fraction of seconds. We are also providing the examples, which are helpful to check whether the result is correct or not.

Simple Method To Find Eigenvalues

One of the best and shortest methods to calculate the Eigenvalues of a matrix is provided here. Checkout the simple steps of Eigenvalue Calculator and get your result by following them.

• Take proper input values and represent it as a matrix.
• Frame a new matrix by multiplying the Identity matrix contains v in place of 1 with the input matrix.
• Find the determinant of the obtained matrix i.e multiplication of the diagonal values of a matrix and subtract the results.
• The above process will form a characteristic polynomial.
• Solve the equation to get the roots.
• The obtained roots are eigenvalues for your input matrix.

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Example:

Question: Find the eigenvalues of a matrix ((-2,-4,2),(-2,1,2),(4,2,5))?

Solution:

Given matrix A= [(-2,-4,2),(-2,1,2),(4,2,5)]

To get the characteristic equation of matrix A, make

A-VI=0, where I is an Identity matrix.

Matrix=[(-2,-4,2),(-2,1,2),(4,2,5)]*[(v,0,0),(0,v,0),(0,0,v)]

Matrix=[(-2-v,-4,2),(-2,1-v,2),(4,2,5-v)]

Det Matrix=0

Det [(-2-v,-4,2),(-2,1-v,2),(4,2,5-v)]= 0

By expanding the determinant:

(-2-v)x[(1-v)x(5-v)-2×2]+4[(-2)x(5-v)-4×2]+2[(-2)x2-4(1-v)]=0

After simplifying

-v³+4v²+27v-90=0

or v³-4v²-27v+90=0

By applying trial and error method, we got

v³-4v²-27v+90=(v-3)(v²-v-30)

(v-3)(v²-v-30)=(v-3)(v+5)(v-6)

That means eigenvalues are 3,-5,6

FAQs on Eigenvalue Calculator

1. Does every matrix have eigenvalues?

Every matrix has an eigenvalue, but it may be a complex number.

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2. What does a zero eigenvalue means?

Geometrically, zero eigenvalue means no information in an axis. We all know that the determinant of a matrix is equal to the products of all eigenvalues. If one or more eigenvalues are zero then the determinant is zero and which is a singular matrix.

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3. Are eigenvalues unique?

Eigenvalues are not unique.

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4. What is the eigenvalue of a matrix?

Eigenvalues are the special set of scalars associated with a linear system of equations known as characteristic roots and values.

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Converting Percentage to GPA Out of 10: Whenever a candidate applies for any undergraduate or graduate or postgraduate or any other programs, a most significant and confusing factor is understanding the considerable difference between CGPA and GPA. In India, the percentage system is most commonly used for grade calculation. Even though it is quite puzzling to convert the percentage to GPA, in the current education system, students’ evaluation using the CGPA system is quite popular in India.

This article contains all the details and descriptions related to the GPA and CGPA systems of evaluating the students in various universities and Percentage to GPA out of 10 Conversion, Percentage to GPA Converter etc. Go through the below links and understand the conversion within no time.

• Diverse Grading Scales
• Comprehension GPA & Its Calculation
• GPA & Indian Grading System
• Percentage System
• GPA System
• How to do Conversion of Percentage to GPA?
• Percentage to GPA Calculator- 4.0 Scale
• Percentage to GPA Calculator 10.0 Scale
• Explanation of GPA Out of 10 Scale
• Conversion of GPA to Percentage
• FAQs on Percentage to GPA Converter
• Conclusion on Converting Percentage to GPA Out of 10 

Various Grading Scales

Before understanding the grade calculation and conversion of the percentage to GPA converter out of 10, we must first focus on the different grading systems available and used in various Indian institutes. Here is a table to explain the grading system of CBSE to GPA Converter in detail:

Grade	GPA	CGPA	Percentage
A+	4	>8.5	85-100
A	3.7	8.0-8.4	80-84
B+	3.3	7.5-7.9	75-79
B	3	7.0-7.4	70-74
B-	2.7	6.5-6.9	65-69
C+	2.3	6.0-6.4	60-64
C	2	5.5-5.9	55-59
C-	1.7	5.0-5.4	50-54
D	1.3	4.5-4.9	45-49
E	1	4.0-4.4	40-44
F	0	0-3.9	0-39

Also Check: Convert CGPA to Percentage

Understanding GPA and Calculating It

GPA (Grade point Average) is a widely known and internationally recognized calculation method for academic marks. Simple, the average or aggregate score of the grades cumulated during the entire duration of any course or program for a fixed period. The GPA system allows any person to read the individual results quickly and efficiently and analyze them compared to others’ results. It is also helpful for people to access their applications and reflect their academic potential and capabilities.

Generally, GPA is calculated by dividing a student’s average grade by the total credit hours that they attended during the fixed period of an academic course or program. The formula for GPA calculation is as follows:

GPA = Total grade points / the Total number of credit hours for a selected course’s fixed period.

GPA and Indian Grading System

In contrast to the GPA grading system, which is prominent in the USA and various other nations globally, the Indian grading system considers two main approaches, i.e., a 10-point GPA system or the percentage system. Here is a brief on both the systems prominently used across several Indian institutions and education boards.

Percentage System

Coming over the percentage method, this is the more preferred evaluation mechanic. In this grading system, the marks for a specified duration are converted to a percentage, and the ranks are then classified as follows:

• 75% = Distinction
• 60% – 75% = 1st Division
• 50% – 60% = 2nd Division
• 40% – 50% = 3rd Division

GPA System

In GPA out of 10 scales, points associates with letter grades for marking the students. For example, if the grade point is 9, the student’s grade will be “A”. This grading system is also quite akin to the international grading system with a 4.0 scale. For example, if a student scores 95%, the result for him/her will be as an A grade, meaning 4.0; 85% would equal to B grade, meaning 3.0; and C grade is 2.0 and D is 1.0.

Conversion of the Percentage to GPA

While considering the USA education system, the students get a rating either out of 0 – 4.0 grade points or follow the 10-point GPA system. Many of the prominent European universities also follow the 10-point GPA system. In specific scenarios, various institutes have different ways of converting percentage to GPA out of 10. The most prominent and widely used and accepted method is multiplying or dividing the score by 9.5 to convert it into percentage or GPA, respectively.

Converting Percentage to GPA for 4.0 Scale

While considering the US grading approach, there is a prominent usage of the 4.0 GPA scale, meaning that if we compare it to the Indian grading system of the percentage that is of 100 (100 points), 25 points in this system equals 1 point in the US GPA grading system. Thus, the formula for converting Percentage to GPA on a 4.0 scale is for merely doing the division of the percentage by 100 and then multiplying the same to 4. Here is the formula for the percentage to GPA converter:

GPA = (percentage/100) * 4

This conversion mechanic is also widely used for doing the GPA to percentage conversion.

Example: Suppose any student scores 70% as the aggregate score in the graduation; while preparing the application for any prominent US-based institute, he/she will have to put the graduation scores in GPA. This the students can calculate by dividing 70% by 100 and then multiplying it by four, and this will make the grade point as 2.8 GPA.

Converting Percentage to GPA for 10.0 Scale

Apart from India, many other nations also use a 10-point GPA system in various schools and institutes. For converting percentage to GPA out of 10, the student can just multiply the percentage by 9.5. The calculation formula for the percentage to GPA conversion is as follows:

GPA = Percentage/ 9.5

Example: If a student secures 85% in any examination, then while applying for any US-based university, the application form might have a field to be filled with the scores in the form of GPA. Thus by converting GPA out of 10, the person who access the application form gets ease in comparing the scores with the other students who graduated from other schools in the USA or any other part of the World. For converting percentage to a 10GPA, the student must divide the percentage secured that is 85%, by 9.5, and the GPA will come out to be 8.9.

A Brief Explanation On GPA Out Of 10 Scale

The GPA scale varies from 0-10, and here 0 means a failure in the test/exam, and 10 means excellent academic results. Here is a brief description of how to analyze the performance of any student in the 10-point GPA grading system:

Score	Details
9-10	Excellent
7.5-8.99	Good
6-7.49	Average
5-5.99	Needs some improvement
0-4.99	Fail

GPA to Percentage Conversion

The widely used formula for GPA to percentage conversion is as follows:

Percentage = GPA * 9.5

For example, if a student has a GPA of 8, multiplying it with 9.5 will give the percentage, i.e., 8 * 9.5 =76%

Must Check: CGPA Calculation for Engineering Students

FAQ’s on Converting Percentage to GPA Out of 10

Question 1.
Calculate GPA of 70%.

Answer:
While considering the 4.0 grading scale, 70% will equal to (70 / 100) * 4, i.e., 2.8 GPA.

And while considering the 10 point grading system, 70% will be converted to GPA as 70 / 9.5 = 7.36.

Question 2.
What is my GPA while considering a 4.0 scale?

Answer:
In a 4.0 GPA grading system, a 4.0-grade point accounts for an A+ or A, followed by 3.0, which accounts for B, 2.0 for C, and 1.0 for D.

If the grade has a plus following it, this means that the student scored an additional one-third of a point, like B+ = 3.3.

On the other hand, if a minus follows the grade, the student scored one-third less than the grade point, like A- = 3.7.

Question 3.
How do we convert percent to GPA?

Answer:
Two main scales are widely standard for converting percentage to GPA, either on a 4.0 scale or on a 10.0 scale. 4.0 scale grading system is widely popular across the university and institutes of the US, while a 10 GPA scale is standard across India.

For converting percentage to GPA on a 4.0 scale grading system, one must divide the percentage scored by 100 and then multiply the resultant by 4 to get the GPA. Here is the formula for converting percent to GPA on a 4-scale:

GPA on 4.0 scale = (Percentage / 100) * 4

For converting percentage to GPA on a 10.0 scale, one must divide the percent by 9.5, i.e.,

GPA on 10.0 scale = Percentage / 9.5

Conclusion on Converting Percentage to GPA Out of 10

Conversion of the percentage to various GPA points and vice versa plays a crucial role while submitting multiple applications according to different universities and institutes from across the World. The article contains a brief on the general methods for completing the processes of Converting Percentage to GPA Out of 10. This is beneficial for students seeking admissions in native colleges and international institutes, and universities. Also, check more conversions like this from Learncram.com

Use this handy Domain and Range Calculator to get the exact answer for your function instantly. All you need to do is enter the function in the input box and press the calculate button which is in blue colour to display the domain and range values of that particular function in seconds.

Domain and Range Calculator: Struggling to find the domain and range of any function. Then you can avail the handy tool Domain and Range Calculator to get the output instantaneously. In the below section, you can check the steps to solve the domain and range for square root function and polynomial function, and others. For your better understanding, we are also giving the example questions.

Steps to get the Domain and Range for Square Root or other Functions

You can observe the simple steps through which we can know the domain and range of any real valued function. Use these steps, when you are searching for a detailed process to solve the domain & range.

• Take any real valued function
• Find any real number for x get a meaningful output
• Domain is all the real numbers, except for which number we are not getting the meaningful output.
• Do the inverse function by interchanging the x and y values
• Again, get the real numbers for which we are getting a meaningful output
• Range is also all the real numbers except those set of numbers for which you are not getting the output.

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How to Find the Domain & Range for Real Valued Function?

• Take any real valued linear function
• We know that real functions are the lines that continue forever in each direction
• Check that by substituting the any real number in the function, gives an output or not
• Then all the real numbers are domain and range

Example

 

Question1: Find the domain and range of the function y=x²-3x-4/x+1

 

Solution

Given function is y=x²-3x-4/x+1

We can say that the function is not defined at x=-1

Because when we substitute -1for x, we get zero in the denominator

So, the domain is all real numbers except -1

Find the factors of numerator

y=(x+1)(x-4)/(x+1)

y=x-4

Substitute the x=-1 in the above equation

y=-1-4

y=-5

This means, the function is not defined when y=-5 and x=-1

Therefore the range of the function is {y belongs to R | y=!-5} and domain is {y belongs to R | x=!-1}

Question2:
What are the domain and range of the function f(x)=-2+sqrt(x+5)?

 

Answer:

Given function f(x)=-2+sqrt(x+5)

This is a radical function

Square root must be always positive or zero

sqrt(x+5)>=0, then -2+sqrt(x+5)>=-2

range is all real numbers such that f(x)>=-2

The domain of the radical equation is any x value for which the sign is not negative.

That means, x+5>=0

x>=-5

FAQs on Domain and Range

1. What is the domain and range?

Domain is a set of all values for which the function is mathematically defined. The range is the set of all possible output values (commonly the variable y or f(x)), which result from using a particular function.

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2. Does every function have a domain?

Yes, every function has a domain.

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3. What is the difference between domain and range?

Domain is all the values that go into function and range is all values that come out.

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4. How do you write domain and range?

Domain and range are always written from smaller to larger values or from left to right for domain and from bottom to the top of the graph for range.

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5. How do you find the domain and range on a calculator?

Enter input in the specified box and click on the calculate button to display output.

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By taking the help of Linear Programming Calculator, you will get the exact solution quickly. You have to provide all your conditions and functions as input in the respective fields and press the calculate button to get the answer in seconds.

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How to Solve Objective functions with Linear Constraints?

Here, you can see the simple guidelines to solve the objective function with the given linear constraints. Follow these steps and compute the maximum and minimum of the functions.

• Take any objective function P and other linear constraints
• Out of all the constraints, compute the conditions which are having two variables for example x and y
• Convert the expression as bring one variable y
• By taking the slope of those constraints draw a graph
• Mark the feasible region and find out the vertices
• Substitute all the values of vertices in the objective function
• Check for which vertices, the function is minimum and maximum

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Example

Question: Find the feasible region for 2x+y=1000, 2x+3y=1500, x=0, y=0 and maximize and minimize for the objective function 50x+40y?

Answer:

Given that,

Objective function f(x,y)=50x+40y

Given constraints are

2x+y=1000, 2x+3y=1500, x=0, y=0

2x+y=1000

y=1000-2x

2x+3y=1500

3y=1500-2x

y=(1500-2x)/3

y=500-2x/3

The graph will be

The shaded area will be the feasible region in the above graph

The vertices are (0,500), (375,250), (500,0)

f(x,y)=50x+40y

Substitute the vertices in the objective function

f(0,500)=50*0+40*500=20,000

f(375,250)=50*375+40*250=28,750

f(500,0)=50*500+40*0=25,000

The minimum value is (0,500)

Maximum values are (275,250)

FAQ’s on Linear Programming

1. What is the process of linear programming?

Linear programming is the process of taking various linear inequalities relating to some situation and finding the best value obtained under those conditions.

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2. What is the linear function and examples?

Linear functions are graphs as a straight line format. The standard form of linear function is y=f(x)=a+bx. It has one dependent variable and one independent variable.

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3. What are the components of linear programming?

The three different equalities or inequalities or components of the linear programming are decision variables, objective function and constraints.

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4. How can you solve the linear programming problem?

Find out the feasible region for the constraints and decision variables. Point out the vertices, and substitute those values in the objective function to get the maximize and minimize values.

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5. How do you solve the maximum value in linear programming?

If linear programming can be optimized, an optimal value will occur at one of the vertices of the region representing the set of feasible solutions.

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Make use of this free handy Inflection Point Calculator to find the inflection points of a function within less time. Just enter function in the input fields shown below and hit on the calculate button which is in blue colour next to the input field to get the output inflection points of the given function in no time.

Inflection Point Calculator: Want to calculate the inflection point of a function in a simple way? Then you must try out this user friendly tool provided. It is one of the easiest ways that you ever find to compute the inflection point of a function. This page is all about Finding Inflection Point of the given function using a simple method and the interactive tutorial explaining each step of the process.

Steps to Find Inflection Point

Follow the below provided step by step process to get the inflection point of the function easily.

• Take any function f(x).
• Compute the first derivative of function f(x) with respect to x i.e f'(x).
• Perform the second derivative of f(x) i.e f”(x) and also solve the third derivative of the function.
• f”'(x) should not be equal to zero.
• Make f”(x) equal to zero and find the value of variable.
• Substitute x value in the third derivative of function to know the minimum and maximum values.
• Replace the x value in the given function to get the y coordinate value.
• Then, inflection points will be (x value, obtained value from function).

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Example

Question: Find the inflection points for the function f(x) = -x⁴ + 6x²?

Solution:

Given function is f(x) = -x⁴ + 6x²

f'(x) = -4x³ + 12x

f”(x) = -12x² + 12

f”'(x) = -24x

f”(x) = 0

-12x² + 12 = 0

12 = 12x²

Divide by 12 on both sides.

1 = x²

x = ± 1

x1 = 1, x2 = -1

Substitute x = ± 1 in f”'(x)

f”'(1) = -24(1) = -24 < 0, then it is left hand bit to right hand bi.

f”'(-1) = -24(-1) = 24 > 0, then it is left hand bit to right hand bit.

Replace x = ± in f(x)

f(1) = -1+6 = 5

f(-1) = -1 +6 = 5

Therefore, inflection points are P1(, 5), P2(-, 5)

FAQs on Inflection Point Calculator

1. How do you find inflection points on a calculator?

Provide your input function in the calculator and tap on the calculate button to get the inflection points for that function.

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2. What does inflection point mean?

Inflection point is defined as the point on the curve at which the concavity of the function changes. It can be a stationary point but not local maxima or local minima.

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3. Find the point of inflection for the function f(x) = x⁵ – 5x⁴?

Given that

f(x) = x⁵ – 5x⁴

f'(x) = 5x⁴ – 20x³

f”(x) = 20x³ – 60x²

f”'(x) = 60x² – 120x

Neccessary inflection point condition is f”(x) = 0

20x³ – 60x² = 0

20x²(x-3) = 0

x1 = 0, x2 = 3

Substitute x2 = 3 in the f(x)

f(3) = 3⁵ – 5*3⁴ = 243 – 405 = -162

Inflection Point is (3, -162).

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4. What is the difference between inflection point and critical point?

A critical point is a point on the graph where the function’s rate of change is altered wither from increasing to decreasing or in some unpredictable fashion. Inflection point is a point on the function where the sign of second derivative changes (where concavity changes). A critical point becomes the inflection point if the function changes concavity at that point.

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Use this online Limit Calculator to know the limit of a function by replacing the variable value. Enter your function and variable value as the inputs in the below fields and get the result by tapping on the calculate button in a fraction of seconds.

Limit Calculator: Are you looking for easy ways to find function limits? Then, stop your search right here because we have come up with a simple method to compute the function limit in the given range. With the help of this handy Limit Calculator tool, you can easily calculate the limit and know the output automatically. Furthermore, you can also check the steps to solve the function limit with a best example and its form.

How to get the Limit of a function?

The limits are used to define the integrals, derivatives, and continuity. The limit function is a concept in the analysis which concerns the behavior of a function at the particular moment. Here we are offering the stp by step process to evaluate a limit function. Checkout the below sections and follow them while calculating a limit function in the given range.

• Take a limit function and substitute the variable value to get the output this is called substitution.
• If the above substitution method fails, then follow this factorization method. Especially, use this method when the function is a polynomial expression.
• Do factorization of the given function, cancel the similar terms and substitute the variable value.
• When a function is having the square root in the numerator and polynomial expression in the denominator, solve it by rationalizing the numerator.
• Solve the expression and substitute the variable value in it.

Basic Form

The standard form to represent the limit function is lim x to c f(x) = L

Where,

C is a real number

f is a real valued function

Example:

Question1: Solve Lim x->5 x^2-6x+8 / x-4?

Answer:

Here we use the substitution method

f(x)=x^2-6x+8 / x-4

f(5) = 5^2 – 6*5 + 8 / 5-4 = 25-30+8 / 1 = 3

Therefore, the solution is 3.

Question2: Solve lim x->4 x^2-6x+8 / x-4?

Answer:

f(x)=x^2-6x+8 / x-4

Substitution process does n’t work here. Because the denominator can’t be zero.

Check out the factorization method

After factorization the f(x) can be as follows

f(x) = (x-4) * (x-2) / (x-4)

After cancelling f(x) = x-2

f(4) = 4-2 = 2

The answer is 2

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Frequently Asked Questions on Limit

1. What is the limit formula?

lim x->a f(x) is the limit formula. This is called the limit of a function f(x) at an interval x=a.

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2. What are the five laws of limits?

The list of limit laws are here.

• Constant Law limx->a k=k.
• Identity Law limx->a x=a.
• Sum Law limx->a f(x)+g(x) = limx->af(x) + limx->ag(x)
• Difference Law limx->a f(x)-g(x) = limx->af(x) – limx->ag(x)
• Constant Coefficient Law limx->a k*f(x) = klimx->af(x)
• Multiplication Law limx->a f(x)*g(x) = limx->af(x) * limx->ag(x)

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3. What is the limit of a constant?

The limit of a constant function is always a constant.

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4. What is the limit?

In maths, a limit is the value that a function approaches as the input and approaches some value.

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5. Solve limx->13 square root (x-4)-3 / x-13 using the rationalizing the numerator process?

After rationalizing the numerator, we will get the expression as 1 / square root of x-4 +3. Substitute the value. the value is 1/16.

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Avail Infinite Series Calculator Over here to solve your complex problems too easily. Simply provide the inputs in the respective input field and tap on the calculate button to get the concerned output.

Infinite Series Calculator: Finding the sum of an infinite series of a function is not so simple or easy for any one. It will have difficult mathematical operations and it consumes your time and energy. So, we are coming up with the best solution for your problem by giving the free handy Infinite Series Calculator tool. You can also get the lengthy manual solution to solve the sum of the infinite series of a function. Make use of this free calculator tool to get accurate solutions for your function quickly.

Steps to find the Sum of Infinite Series of Function

Learn about how to solve the sum of infinite series of a function using this simple formula. Follow the below provided step by step procedure to obtain your answer easily.

• Take any function with the range to infinity to solve the infinite series
• Convert that function into the standard form of the infinite series
• Apply the infinite series formula
• Do all the required mathematical calculations to get the result

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Standard Form of Infinite Series

Infinite series is defined as the sum of values in an infinite sequence of numbers. The notation Sigma (Σ) is used to represent the infinite series. The standard form of infinite series is

Σ₀ ^∞ rⁿ

Where 0 is the lower limit

∞ is the upper limit

r is the function

The formula to find the infinite series of a function is defined by

Σ₀^∞ rⁿ = 1/(1-r)

Example:

 

Question: solve the sum of Σ₀^∞ 1/10ⁿ?

 

Solution:

Given function is 1/10ⁿ

r=1/10

Infinite series formula is

Σ₀^∞ rⁿ = 1/(1-r)

Σ₀^{∞ 1/10n=1/(1-1/10)}

=10/9

Σ₀^{∞ 1/10n=10/9}

Frequently Asked Questions on Infinite Series Calculator

1. Can an infinite series be calculated?

We can calculate the sum of an infinite geometric series. The formula to solve the sum of infinite series is related to the formula for the sum of first n terms of a geometric series. Finally, the formula is Sn=a1(1-r^n)/1-r.

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2. What is the general formula for the sum of infinite geometric series?

The formula to find the sum of an infinite geometric series is S=a1/1-r.

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3. What is r in a sequence?

r is called common ratio. The number multiplied or divided at each stage of a geometric seque is the common ratio.

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4. What are the 4 types of sequences?

Some of the sequences are Arithmetic Sequences, Geometric Sequences, Harmonic Sequences, and Fibonacci Numbers.

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5. What is meant by sequence and series?

Sequence is a list of numbers that have been ordered sequentially. Series is defined as the sum of the sequence terms.

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