Chapter 9.1, Problem 8E

Linear and quadratic approximation

1. a. Find the linear approximating polynomial for the following functions centered at the given point a.
2. b. Find the quadratic approximating polynomial for the following functions centered at the given point a.
3. c. Use the polynomials obtained in parts (a) and (b) to approximate the given quantity.

8. $f(x)=\frac{1}{x}$, a = 1; approximate $\frac{1}{1.05}$.