Linear approximation is a mathematical method for approximating the value of a function near a specific point. It involves using the tangent line at the point to approximate the value of the function.
Linear approximation is used in various fields, such as physics, engineering, and economics, to estimate the behavior of a system or process near a specific point. It is also used in financial modeling and forecasting.
While both methods involve estimating the value of a function, linear approximation uses the tangent line at a specific point, while linear interpolation uses a line connecting two known data points to estimate the value at an unknown point.
Linear approximation is only accurate near the chosen point and becomes less accurate as the distance from the point increases. It also assumes that the function is continuous and differentiable at the point.
To calculate linear approximation, you will need the value of the function at the chosen point and the slope of the tangent line at that point. You can then use the formula y = f(a) + f'(a)(x-a) to find the approximate value of the function at a nearby point x.