Checkpoint 5 Answers

1. There are two parts of the simplification: First, ${\displaystyle {\left|x\right|}^{2n+3}={\left|x\right|}^2{\left|x\right|}^{2n+1}}$. Second, ${\displaystyle (2n+3)!=(2n+3)(2n+2)(2n+1)\cdots 3\cdot 2\cdot 1=(2n+3)(2n+2)(2n+1)!}$.
2. 0.0233
3. -0.93758
4. ${\displaystyle sin 5=-0.95892}$. The actual error is 0.0213. Thus the error bound is fairly close — within about 10% of the actual error.