# Linear Approximation Calculator

## Now, What Exactly Is A “Linear Approximation Calculator”?

A linear approximation calculator is a tool that helps you find the value of a certain variable by approximating it with a linear function.

## Free Linear Approximation Calculator With Steps

This is a very simple tool for Linear Approximation Calculator. Follow the given process to use this tool.

☛ Step 1: Enter the complete equation/value in the input box i.e. across “Provide Required Input Value:”

☛ Step 2: Click “Enter Solve Button for Final Output”.

☛ Step 3: After that a window will appear with final output.

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## Formula for linear approximation

The linear approximation formula can be used to approximate a nonlinear function by a linear function. The formula is:

y = f(x) + f'(x) * (x – a)

Where y is the approximate value, f(x) is the original function, f'(x) is the derivative of f(x), and a is the point at which the approximation is being made.

## Linear Approximation Definition

Linear approximation is a mathematical concept used to describe the relationship between two variables that are evenly distributed around a central value. The linear approximation is the arithmetic mean of the two outermost values in a distribution.

## Example of linear approximation based on Formula

The linear approximation of a function f(x) at a point x0 is given by the formula:

f(x) ≈ f(x0) + f'(x0)(x – x0)

where f'(x0) is the derivative of f(x) at x0.

For example, if the function f(x) is given by f(x) = x2 and the point x0 is given by x0 = 1, then the linear approximation of f(x) at x0 is given by f(x) ≈ f(x0) + f'(x0)(x – x0) = f(1) + f'(1)(x – 1) = 1 + 2(x – 1) = 2x – 1.