Section 11.10 A

Key Problems: 11-16, 21, 22

Problem 11

Find the Maclaurin series for $f(x)$ using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that $R_n(x)\to 0$ ] Also find the associated radius of convergence.

$$f(x)=(1-x{)}^{-2}$$

Problem 12

$$f(x)=\ln (1+x)$$

Problem 13

$$f(x)=\cos x$$

Problem 14

$$f(x)=e^{-2x}$$

Problem 15

$$f(x)=2x^4-3x^2+3$$

Problem 16

$$f(x)=\sin 3x$$

Problem 21

Find the Taylor series for $f(x)$ centered at the given value of a. [Assume that f has a power series expansion. Do not show that $R_n(x)\to 0$.] Also find the associated radius of convergence.

$$f(x)=x^5+2x^3+x,a=2$$

Problem 22

$$f(x)=x^6-x^4+2,a=-2$$