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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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Enter your equation and data items in the input box and click on the calculate button to obtain the Implicit Differentiation for your equation. Use this handy free online Implicit Differentiation Calculator tool to get the accurate output of an equation in a fraction of seconds.

Implicit Differentiation Calculator: If you want to calculate implicit differentiation of an equation use this handy calculator tool. It is not easy for anyone to find the implicit differentiation at the given point. So, to assist you in this we are giving the lengthy manual step by step process to solve the implicit differentiation of the equation. Here, we are also giving an example for your better understanding.

Steps to Solve Implicit Differentiation of Equation

The simple and easy procedure to find the implicit differentiation of the equation is mentioned below. Go through the step by step process and follow them while solving the equation.

• Let us take any polynomial equation contains two variables x and y
• Apply the differential function on the both sides of the equation i.e dy/dx
• Calculate the derivatives
• Bring dy/dx on the one side of the equation
• Do the mathematical operations to the dy/dx value
• Substitute given (x,y) values in the obtained expression
• The obtained number is your answer.

Example

Solve Implicit Differentiation of x³+y³=2xy at (x,y)=(2,3)?

Solution:

Given equation is

x³+y³=2xy

Derivative of the equation is

dy/dx(x³)+dy/dx(y³)=dy/dx(2xy)

3x²+3y²dy/dx=2xdy/dx+2y

3y²dy/dx-2xdy/dx=2y-3x²

dy/dx(3y^2-2x)=2y-3x^2

dy/dx=2y-3x²/3y²-2x

dy/dx at (2,3) is substitute x=2 and y=3 in the above equation

=2(3)-3(2)²/3(3)²-2(2)

=6-12/27-4

=-6/23

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FAQs on Implicit Differentiation Calculator

1. Why do we use implicit differentiation?

Implicit differentiation technique allows you to find out the derivative of y with respect to x without having to solve the general equation for y.

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2. What is the implicit differentiation of xy?

The implicit differentiation of xy is

dy/dx(xy)=xy’+x’y

=xy’+y

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3. What are the differences between implicit differentiation and partial differentiation?

In implicit differentiation, all the variables are differentiated. In partial differentiation, the derivative is done only one variable by leaving other variables as constants.

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4. What is meant by implicit function?

Implicit function is a function where dependent and independent variables are kept on one side of the equation.

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Free handy Triple Integral Calculator is here to calculate the triple integral of a function within a short span of time. Just provide the input function and bounds in the input section of the calculator and press on the calculate button to get the result immediately.

Triple Integral Calculator: If you are struggling to figure out the triple integral of a function you have come the right way. Take the help of our free Triple Integral Calculator tool to get the instant output for your expression. Along with this calculator, you can also learn the step by step procedure to solve the triple integral function easily. For your better understanding we have also provided an example question in the below sections.

Steps to Solve Triple Integral Function

Triple integral is similar to double integral. In triple integral, you need to calculate the integration for three different variables with respect to three variables. Check the following module to get an idea on how to solve the triple integral. Follow these guidelines and compute the function simply.

• Take any function have three variables to solve the triple integral
• First you need to perform the integration with respect to one variable to eliminate that variable.
• After integration substitute the bound values in the expression i,e upper limit – lower limit
• Important point is while performing integration with respect to one variable, you need to consider the other two variables as constants.
• After eliminating the first variable, you have to repeat the process in the same way to eliminate the remaining variable and get your answer in constant.

Example

Question: Solve ∫₀³∫₂³ ∫₁² x²y²z² dxdydz?

Solution:

Given that

∫₀³ ∫₂³ ∫₁² x²y²z² dxdydz

At first, perform integration with respect to x

∫₀³ ∫₂³ x³/3*3y²z² dydz

Substitute the limit values in obtained expression

∫₀³ ∫₂³ y²z² dydz [2³-1³/3]

=∫₀³ ∫₂³ y²z² dydz [8-1/3]

=∫₀³ ∫₂³ y²z² dydz [7/3]

Calculate integration with respect to y

=∫₀³ y³/3*7z²/3 dz

=∫₀³ 7z²/3 dz [3³-2³/3]

=∫₀³ 7z²/3 dz [27-8/3]

=∫₀³ 7z²/3 dz [19/3]

=∫₀³ 133z²/9 dz

Now, perform integration with respect to z

=133/9 * z³/3

Replacing the bound values

=133/9 * [3³-0³/3]

=133/9 * 27/3

=133

=133

∫₀³∫₂³ ∫₁² x²y²z² dxdydz= 133

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FAQs on Triple Integral Calculator

1. Where we can use triple integrals?

Triple integrals are the analog of double integrals for three dimensionals. They are used to find the volume of a three dimensional space and for adding up infinity quantities associated with points in a three dimensional region.

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2. Is triple integral volume?

Triple integrals are used to find volume, just like double integrals are used to find mass, when volume of the region has variable density.

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3. How do you find the volume of a triple integral?

The volume of an ellipsoid is expressed using the triple integral which is V=∭U dxdydz=∭U′abcρ2sinθdρdφdθ. By symmetry, you can find the volume of ellipsoid lying in the first octant (x≥0, y≥0, z≥0) and multiply the result by 8.

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4. How to compute Triple Integrals?

Solving triple integrals is the same as double integrals. Here, you need to solve the integration of three variables in the given range. Solve the integration and substitute the range value in the obtained expression to get the answer.

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We are pretty sure you can easily find the Maclaurin Series of a function easily using our free Maclaurin Series Calculator tool. Just enter your input function and range values in the specified input fields and hit the calculate button to check the Maclaurin series of function in a fraction of seconds.

Maclaurin Series Calculator: Do you feel solving Maclaurin Series of function is difficult? Then you are on the right place. You can get the step by step procedure to solve the maclaurin series function in a shot span of time. This Maclaurin Series Calculator gives the answer for your question immediately. Go through the following sections to get a clarity on the Maclaurin Series.

Steps to Compute Maclaurin Series of Function

Below mentioned are the simple and easy steps that are helpful while solving the maclaurin series function. Follow these guidelines

• Take any function and its range to solve the Maclaurin Series.
• For any function f(x) the maclaurin series is given by f(x)=∑_k=0^∞ f^(k) (a)* x^k/ k!
• Find f^(k) (a) by calculating the function derivative and substituting the range values in the function.
• Compute the k! for each step.
• Replace the values in the above formula.
• Apply sigma function and obtain the answer.

Example

Question: Calculate Maclaurin Series of sin(x) up to n = 5?

Solution:

Given function f(x)= Sin(x)

n = 0 to 5

Maclaurin series for the function is f(x)=∑_k=0^∞ f^(k) (a)* x^k/ k!

f(x)≈ ∑_k=0⁵ f^(k) (a)* x^k/ k!

So, calculate the derivative and evaluate them at the given point to get the result into the given formula.

f⁰(x) = f(x) = sin(x)

Evaluate function: f(0) = 0

Calculate first derivative f¹(x) = [f⁰(x)]’

= [sin(x)]’ = cos(x)

[f⁰(x)]’ = cos(x)

Evaluate first derivative (f(0))’ = cos(0) = 1

Second Derivative: f²(x) = [f¹(x)]’ = [cos(x)]’ = -sin(x)

(f(0))′′=0

Third derivative: f³(x) = [f²(x)]’ = (-sin(x))’ = -cos(x)

Evaluate third derivative (f(0))”’ = -cos(0)

= -1

Fourth derivative: f⁴(x) = [f³(x)]’ = [-cos(x)]’ = sin(x)

Evaluate 4th derivative (f(0))”” = sin(0) = 0

Fifth derivative: f⁵(x) = [f⁴(x)]’ = [sin(x)]’ = cos(x)

Evaluate 5th derivative (f(0)””’ = cos(0) = 1

Replace the derivative values in the above formula

f(x) ≈ 0/0! x⁰ + 1/1! x¹ + 0/2! x² + (-1)/3! x³ + 0/4! x⁴ + 1/5! x⁵

f(x) ≈ 0 + x + 0 – 1/6 x³ + 0 + 1/120 x⁵

sin(x) ≈ x-1/6 x³ + 1/120 x⁵

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Frequently Asked Questions on Maclaurin Series

1. How do you define the Maclaurin Series?

Maclaurin Series is defined as the expanded series of the function. Here, approximate value of the function can be evaluated as the sum of derivatives of the function.

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2. What is the difference between Maclaurin and Taylor Series?

Taylor Series is the representation of a function as an infinite sum of terms calculated from the values of its derivatives at a single point. Maclaurin series is a special case of tayloe series which uses zero as a single point.

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3. How does Maclaurin series work?

A maclaurin series is a power series that allows you to calculate an approximation of function f(x) for the input values close to zero, given that one knows the values of the successive derivatives of the function at zero.

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4. What is the formula of Maclaurin series?

Maclaurin series for function is defined as f(x)=∑_k=0^∞ f^(k) (a)* x^k/ k!

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Indefinite Integral Calculator directly gives the integral of your input function easily in fraction of seconds. Just enter function as the input in the specified fields and tap on the calculate button which is available next to the input section to find the result in seconds.

Indefinite Integral Calculator: Do you feel calculating indefinite integral somewhat difficult? Not anymore with the help of our easy to use online calculator tool. Now, you can solve the integration of any function easily and instantly by using our Indefinite Integral Calculator. Refer the below section, to get familiar with this concept by checking the solved examples. The step by step process to compute the indefinite integral is also mentioned here.

Procedure to Find Indefinite Integral of Function

Use online and handy Integration By Parts Calculator to get the exact answer after integrating your function. All you have to do is provide the input expression and click on the calculate button to display the related output in no time.

Integration By Parts Calculator: Want to calculate the integration by parts of an expression in an easy way? Then you must go through the below sections of this page. Here, we are offering the simple and easy method to solve the integration of an expression by parts.

This page is all about calculating integration of an expression using Integration by Parts Calculator and the interactive tutorial explains each and every step of the process. This free calculator is easy to use because it is having the flexible user interface which helps to explore more about the concepts.

Looking for a tool that does Partial Derivation easily? Utilize our Partial Derivative Calculator tool and obtain the result instantly. Provide input function in the input fields and click on the calculate button to get the partial derivative of the given function along with the detailed solution.

Partial Derivative Calculator: Are you scared of finding the partial derivatives? To help you in this we have given the free Partial Derivative Calculator that does all your derivative calculations in fraction of seconds. We have included the step by step procedure on how to solve the partial differential equation. You can use this online calculator tool to verify whether your answers are accurate or not after performing partial derivative function.