Free Printable Maclaurin and Taylor Series

1.

Maclaurin series has center at __________.

a)

x = 0

b)

x = 1

c)

x = e

d)

x = c

2.

Taylor series has center at _________.

a)

x = 0

b)

x = 1

c)

x = e

d)

x = c

3.

Which is the formula of Maclaurin series?

a)

$\sum_{n=0}^{\infty}\frac{f^{\left(n\right)}\left(0\right)x^n}{n!}$

b)

$\sum_{n=0}^{\infty}\frac{f^{\left(n\right)}\left(c\right)\left(x-c\right)^n}{n!}$

c)

$\sum_{n=1}^{\infty}\frac{f^{\left(n\right)}\left(0\right)x^n}{n!}$

d)

$\sum_{n=1}^{\infty}\frac{f^{\left(n\right)}\left(c\right)\left(x-c\right)^n}{n!}$

4.

Which is the formula of Taylor series?

a)

$\sum_{n=0}^{\infty}\frac{f^{\left(n\right)}\left(0\right)x^n}{n!}$

b)

$\sum_{n=0}^{\infty}\frac{f^{\left(n\right)}\left(c\right)\left(x-c\right)^n}{n!}$

c)

$\sum_{n=1}^{\infty}\frac{f^{\left(n\right)}\left(0\right)x^n}{n!}$

d)

$\sum_{n=1}^{\infty}\frac{f^{\left(n\right)}\left(c\right)\left(x-c\right)^n}{n!}$

5.

Which is the basic Taylor series for $e^x$ ?

a)

$\sum_{n=0}^{\infty}x^n$

b)

$\sum_{n=0}^{\infty}\frac{\left(-1\right)^nx^{2n}}{\left(2n\right)!}$

c)

$\sum_{n=0}^{\infty}\frac{\left(-1\right)^nx^{2n+1}}{\left(2n+1\right)!}$

d)

$\sum_{n=0}^{\infty}\frac{x^n}{n!}$

6.

Which is the basic Taylor series for $\sin x$ ?

a)

$\sum_{n=0}^{\infty}x^n$

b)

$\sum_{n=0}^{\infty}\frac{\left(-1\right)^nx^{2n}}{\left(2n\right)!}$

c)

$\sum_{n=0}^{\infty}\frac{\left(-1\right)^nx^{2n+1}}{\left(2n+1\right)!}$

d)

$\sum_{n=0}^{\infty}\frac{x^n}{n!}$

7.

Find the Maclaurin polynomial with degree n = 2 of $f\left(x\right)=e^{3x}$ .

a)

$1+x+x^2$

b)

$1+3x+6x^2$

c)

$1+3x+\frac{9}{2}x^2$

d)

$1+3x+9x^2$

8.

Find the Maclaurin polynomial with degree n = 5 of $f\left(x\right)=\sin2x$ .

a)

$x+x^3+x^5$

b)

$x-x^3+x^5$

c)

$2x+\frac{8}{3!}x^3+\frac{32}{5!}x^5$

d)

$2x-\frac{8}{3!}x^3+\frac{32}{5!}x^5$

9.

Find the Taylor polynomial with degree n = 3 of $f\left(x\right)=\frac{1}{x}$ centered at c = 1.

a)

$0+x-\frac{1}{2!}x^2+\frac{2}{3!}x^3$

b)

$0+\left(x-1\right)-\frac{1}{2!}\left(x-1\right)^2+\frac{2}{3!}\left(x-1\right)^3$

c)

$1-\left(x-1\right)+\left(x-1\right)^2-\left(x-1\right)^3$

d)

$1+\left(x-1\right)-\left(x-1\right)^2-\left(x-1\right)^3$

10.

Find the Taylor polynomial with degree n = 2 of $f\left(x\right)=\ln\left(x+1\right)$ centered at c = 1.

a)

$\ln2+\frac{1}{2}\left(x-1\right)-\frac{1}{8}\left(x-1\right)^2$

b)

$\ln2+\frac{1}{2}\left(x-1\right)+\frac{1}{4}\left(x-1\right)^2$

c)

$\ln2+\frac{1}{2}x-\frac{1}{8}x^2$

d)

$\ln2+\frac{1}{2}x+\frac{1}{4}x^2$

Maclaurin and Taylor Series

Total questions: 10

Worksheet time: 12mins

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