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Calculus II: Taylor and Maclaurin Series

Total questions: 3

Worksheet time: 14mins

Name
Class
Date
1.

Determine whether it is TRUE or FALSE n=0(1)nn!=1e\sum_{n=0}^{\infty}\frac{\left(-1\right)^n}{n!}=\frac{1}{e}

a)

TRUE

b)

FALSE

2.

Determine the radius of convergence of a function: f(x)=tan1(x2)f\left(x\right)=\tan^{-1}\left(x^2\right) . Radius of convergence is equal to ____ (You may use the Maclaurin series reference)

a)

1

b)

\infty

c)

2

d)

0

3.

Determine the sum of the series: 1ln2+(ln2)22!(ln2)33!+(a)<spanclass=1-\ln2+\frac{\left(\ln2\right)^2}{2!}-\frac{\left(\ln2\right)^3}{3!}+ (a) <span class=

Please write in a fraction a/b or in the smallest decimal form