Chapter 9.1, Problem 97E

Approximating square roots Let p₁ and q₁ be the first-order Taylor polynomials for $f(x)=\sqrt{x}$ centered at 36 and 49, respectively.

1. a. Find p₁ and q₁.
2. b. Complete the following table showing the errors when using p₁ and q₁ to approximate f(x) at x = 37, 39, 41, 43, 45, and 47. Use a calculator to obtain an exact value of f(x).

x	$|\sqrt{x}-p_1(x)|$	$|\sqrt{x}-q_1(x)|$
37
39
41
43
45
47

1. c. At which points in the table is p₁ a better approximation to f than q₁? Explain this result.