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Linear Aproximation Calculator Online

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The Linear Approximation Calculator is a mathematical tool used to estimate the value of a function at a certain point by approximating it as a linear function. It operates on the principle of linearization, enabling users to predict the value of a function at a specific point by using the function’s derivative at another known point.

Formula of Linear Aproximation Calculator

The formula used by the Linear Approximation Calculator is:

f(x) ≈ f(a) + f'(a)(x – a)

Where:

  • f(x) represents the original function to be approximate.
  • a is the point where the approximation is made.
  • f(a) is the value of the original function at point ‘a’.
  • f'(a) denotes the derivative of the original function evaluated at ‘a’.
  • x is the value at which the approximate value of f(x) is you require.
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Table of General Terms

TermDefinition
Original Function (f)The primary function for which approximation is done.
Point (a)The specific point at which approximation is made.
Derivative (f'(a))The rate of change of the original function at ‘a’.
Approximated ValueThe estimated value of the function at point ‘x’.

Example of Linear Aproximation Calculator

Let’s consider a quadratic function f(x) = x^2. At point a = 2, f(a) = 4. The derivative of f(x) = x^2 at a = 2 is f'(a) = 4. If we wish to approximate f(3), applying the linear approximation formula:

f(3) ≈ f(2) + f'(2)(3 – 2) = 4 + 4 * (3 – 2) = 8

Hence, the approximate value of f(3) using linear approximation is 8.

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Most Common FAQs

Q: How accurate is the Linear Approximation method?

A: The accuracy depends on how well the linear function approximates the original function in the vicinity of point ‘a’. Closer the point ‘x’ to ‘a’, higher the accuracy.

Q: Can the Linear Approximation Calculator handle all types of functions?

A: Linear approximation works well for functions that can be linearly approximate near the chosen point ‘a’. However, for functions with highly nonlinear behavior, the accuracy might vary.

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