What is linear approximation?

Linear approximation is a method used in mathematics to estimate the value of a function near a particular point by considering the tangent line at that point.

To use linear approximation, you first find the equation of the tangent line to the function at the given point. This tangent line represents the best linear approximation of the function near that point.

The linear approximation formula is given by: f(x) ≈ f(a) + f'(a)(x - a) where f(x) is the function being approximated, f(a) is the value of the function at the point a, and f'(a) is the derivative of the function at a.

Linear approximation is useful in various contexts such as in calculus, physics, engineering, and economics. It allows us to estimate the behavior of a function without having to perform complex calculations.