Taylor Series

• $0<x<2$

• $0\le x\le2$

• $-2<x\le0$

• $-2\le x<0$

• $-2\le x\le0$

A series expansion of $\frac{\sin t}{t}$  is

•  $1-\frac{t^2}{3!}+\frac{t^4}{5!}-\frac{t^6}{7!}+...$  

•  $\frac{1}{t}-\frac{t}{2!}+\frac{t^3}{4!}-\frac{t^5}{6!}+...$  

•  $1+\frac{t^2}{3!}+\frac{t^4}{5!}+\frac{t^6}{7!}+...$  

•  $\frac{1}{t}+\frac{t}{2!}+\frac{t^3}{4!}+\frac{t^5}{6!}+...$  

•  $t-\frac{t^3}{3!}+\frac{t^5}{5!}-\frac{t^7}{7!}+...$  

The coefficient of x³ in the series for e^3x about x=0 is

• 1/6

• 1/3

• 1/2

• 3/2

• 9/2

• $-3<x\le3$

• $-3\le x\le3$

• $-2<x<4$

• $-2\le x<4$

• $0\le x\le2$

The coefficient of x6 in the Taylor series expansion about x=0 for $f\left(x\right)=\sin\left(x^2\right)$  is

•  $-\frac{1}{6}$  

• 0

•  $\frac{1}{120}$  

•  $\frac{1}{6}$  

• 1

graphing calc question

• 0.369

• 0.585

• 2.400

• 2.426

• 3.426

• A

• B

• C

• D

• E

• A

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• E

What are all the values of x for which the series $\sum_{n=1}^{\infty}\frac{\left(x+2\right)^n}{\sqrt{n}}$  converges?

•  $-3<x<-1$  

•  $-3\le x<-1$  

•  $-3\le x\le-1$  

•  $-1\le x<1$  

•  $-1\le x\le1$  

Graphing Calc Question

• A

• B

• C

• D

• E