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What Is a Local Linear Approximation Calculator?

It is a free online tool that can derive the linear approximation formula for a given function and use it to calculate the approximate values. A linearization calculator incorporates some of the popular numerical techniques, such as Ranga Kutta methods and Euler’s Method. 


 

In the linearization of a function calculator, computations are on the proximity of the tangent line to the graph of the specified function around a particular point. You can use linear approximation to estimate solutions to ordinary differential equations.

 

Linearization Formula

Now, for us to find the multivariable linear approximation of a function f at a point x = a, we should have two things in mind:

  • m, which is the slope of the line
  • A single point that the line goes through, (a, b)

These two will give us the equation of the line.

  • y – b = m(x–a)

In such problems, the values of b or m will not be provided. That is where you have to use the linear approximation steps to find them. 

  • First, take m = f ‘(a), 
  • Then, b = f(a), 

When we collate all these to find the value of y using a linear approximation multivariable calculator, the formula will be as follows:

  • y – b = m(x–a)
  • y = b + m(x–a)
  • m(x–a)
  • y = f (a) + f `(a)(x-a)

With the formula, you can now estimate the value of a function, f(x), near a point, x = a.

How To Do Linear Approximation

The 3d linear approximation calculator or multivariable linear approximation calculator is used in many fields of science. You will have to incorporate a bit of calculus to find a derivative. Here is how to find linearization using the formula derived above:

Example

Find the value of the f (3.5) using the linear approximation at a=2, whose function f(x) is differentiable such that f(3)= 12, and f’(3) = -2.

Solution:

The linear approximation formula is

f(x) ≈ L(x) = f(a) + f’(a)(x-a)

When the values are substituted in the formula, here is what we get

L(x) = f(3) + f’(3)(x-3) = 18-2x

Hence, f(3.5)= 18-2(3.5)

f(3.5)= 18 – 7

f(3.5) = 11

But with the linear approximation calculator, you can arrive at the answer in a blink of an eye with the following steps.

How To Use The Linear Approximation Online Calculator

Follow the steps below to find your approximate values on our linear approximation calculator:

  • First, key in the function, variable and its expansion point in the input fields provided
  • Then click the “Find the Linear Approximation” button to find your answer
  • Lastly, the linear approximation for the given function will appear in a new window

Calculus or algebra doesn’t have to feel like rocket science anymore. 

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