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Session 24: Examples of Linear Approximation | Single Variable Calculus | Mathematics | MIT OpenCourseWare

Linear Approximations | Equation & Examples

Extension: Error Analysis in Linear Approximation - Expii

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SOLVED:In Exercises 55-58, use a CAS to estimate the magnitude of the error in using the linearization in place of the function over a specified interval 1. Perform the following steps a. Plot the function f over I b. Find the linearization L of the function at the point a . c. Plot f and L together on a single graph. d. Plot the absolute error |f(x)-L(x)| over I and find its maximum value. e. From your graph in part (d), estimate as large a δ>0 as you can, satisfying |x-a|<δ ⇒ |f(x)-L(x)|<ϵfo