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# Linear Aproximation Calculator Online

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.

### 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.

### 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.