Linear Approximation Calculator





Please wait.. loading-icon


More Calculators

Introduction to the Linear Approximation Calculator

An approximate calculator is an online freely available tool for finding the approximate value of the given function. The linearization at a point calculator finds the linear approximation of the given function.

linear approximation calculator with steps

This calculator is free of cost without any subscription charges before and after its use. This calculator saves precious time for the user by giving them quick and accurate results.

The user interface of the approximate value calculator is very user-friendly and it is easy to use. It gives the result in no time.

But right after finding the value of a function, you may also check either the point is maxima or minima by using our extreme points calculator.

What do you Know About Linearization Calculator

Approximate calculator is an online tool that is based on the linear approximation process. This calculator is based on the process that simplifies the complex function into a linear approximation function.

The linear approximation calculator is based on the method in which the equation of the tangent line is fixed. This is the best tool for finding the approximation value of the function.

Note: If you're interested in understanding the slope of curved lines, be sure to check out our slope of a curve calculator for deeper insights into the world of calculus.

Formula used by the Approximation Value Calculator

The tangent line approximation calculator is a tool for finding the value f(x) nearest to any point which is x=a. this method is also known as tangent line approximation. A tangent is a plane or line that dissects a curved body at a particular point.

Following is the formula of linearization used in this calculator:

$$ L(x) \;=\; f(a) + f'(a)(x-a) $$

You can either use this formula for doing your manual calculations as well, if you not willing to calculate with our linearization calculator.

How to Use this Linear Approximation Calculator?

The approximate value calculator gives accurate results with step-by-step instructions. The differential approximation calculator usually follows the following steps to calculate the linear approximation values for the given function:

Step 1: Enter the function in the "Equation Box".

Step 2: Enter the function at which you wish to find the linear approximation of the function.

Step 3: Click on the "CALCULATE" button.

After clicking the button, the results will shown on calculator with all possible steps and calculations. Furthermore if you're curious about diving deeper into advanced calculus, you can also explore our high derivative calculator for more insights into higher-order derivatives.

How to Find the Differential Approximation Calculator?

The linearization calculator is a very convenient tool for finding approximation values for the given function. These are the possible ways to get this tool online.

  1. Search on Google, Bing or on Yandex by using the words like "linear approximation calculator" or "linearization calculator". Google will show you number of calculators, you may identify one of the best fit for you by reading the instructions.
  2. Secondly, you can bookmark the differentiation calculator with steps and find this approximate value calculator from here.

In this way, you can find this calculator easily. Also you may find more new calculators like normal line calculator using the above instructions.

Benefits of Tangent Line Approximation Calculator

The linearization at a point calculator is an online tool that is essential to approximate the function in derivation. It is an important tool that is also used in physics as well as mathematics.

Following are some of the benefits of using this online tool:

  • When you solve for math problems, it is fact that errors are always happen. While solving problems manually, you can face multiple errors in it. But this linearization calculator provides 100% accurate and reliable results.
  • Secondly, our calculator is one of the freely available tool on internet. Because we know students can't afford premium plans during the educational tenure of their lifes.
  • Due to great load of studies, students need stress relieving way to get their assignments and homeworks. When they will approach this approximate value calculator that provide step by step solution along with graphs, they will get much precise way of learning.
  • The user-interface of this calculator is quite friendly and easily understandable.

Frequently Asked Question

How to do Linear Approximation

Doing the linear approximation is easy using the linear approximation error calculator as it uses some simple steps,

  • Firstly, choose a point near the function you want to approximate.
  • Now determine the slope of the function on that point.
  • Use the point-slope form and write the equation at the chosen point.
  • Now approximate the function by using the equation.

What is Linear Approximation

Linear approximation is a method to approximate the value of a function near a specific point. In linear approximation, an equation is used to find the tangent line at that point. Due to this, linear approximation is also called as the tangent line approximation or linearization. This equation is also used by linearize calculator.

How to Find Linear Approximation

Finding the linear approximation is easy because of linearize equation calculator which gives steps to solve it. These steps are as follows,

  • Choose a point near which you want to approximate the given function.
  • Calculate the slope of the given function by determining its derivative and write the equation of tangent line using the point-slope form
  • Now apply the equation of linear approximation which is
  • $$ L(x) \;=\; f(a) + f’(a)(x - a) $$

How to Know if Linear Approximation is Over or Under

To know whether the linear approximation is over or under, linearisation calculator compares the value of the function at a point of interest to the point of linear approximation, here are some steps:

  • Calculate the function f(x) and the point of the interest x = a.
  • Now calculate the linear approximation on the same point.
  • If the function’s value on the point of interest is greater than the linear approximation on the point then the approximation is under the function but if the function’s value is lesser than the linear approximation then the approximation overestimates the function.

Is Linear Approximation the Same as Tangent Line

Yes, linear approximation is the same as the tangent line of the function at a specific point. This is because the linear approximation is about calculating the equation of a straight line. This line closely approximates the behavior of the function. The approximation here is achieved using the tangent line of the function.

Tangent line is a straight line at a point that touches the curve of the point on the point. It is the same slope as the function at that point. In linearization of a function calculator, The tangent line equation is used to find the behavior of the function. Hence, the tangent line and linear approximation are closely related to each other.