Problem 12E

Linear and quadratic approximation

a. Find the linear approximating polynomial for the following functions centered at the given point a.

b. Find the quadratic approximating polynomial for the following functions centered at the given point a.

c. Use the polynomials obtained in parts (a) and (b) to approximate the given quantity.

f(x)= tan−1 x, a = 0; approximate tan−1 0.1.

Solution 12E

Step 1:

We need to find the linear and quadratic approximating polynomial for

The linear approximation for at is given by

The Quadratic Approximation for a function y = f(x) based at a point a is given by