Chapter 9.1, Problem 96E

Approximating In x Let f(x) = ln x and let p_n and q_n be the nth-order Taylor polynomials for f centered at 1 and e, respectively.

1. a. Find p₃ and q₃.
2. b. Graph f, p₃, and q₃ on the interval (0, 4].
3. c. Complete the following table showing the errors in the approximations given by p₃ and q₃ at selected points.

x	|ln x − p3(x)|	|ln x − q3(x)|
0.5
1.0
1.5
2
2.5
3
3.5

1. d. At which points in the table is p₃ a better approximation to f than q₃? Explain your observations.