Maclaurin and Taylor Series

Maclaurin series has center at __________.

• x = 0

• x = 1

• x = e

• x = c

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.APR.A.1

Taylor series has center at _________.

• x = 0

• x = 1

• x = e

• x = c

Which is the formula of Maclaurin series?

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

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

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

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

Tags

CCSS.HSF.IF.C.8

Which is the formula of Taylor series?

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

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

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

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

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

•  $\sum_{n=0}^{\infty}x^n$  

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

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

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

Tags

CCSS.HSF.LE.A.2

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

•  $\sum_{n=0}^{\infty}x^n$  

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

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

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

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

•  $1+x+x^2$  

•  $1+3x+6x^2$  

•  $1+3x+\frac{9}{2}x^2$  

•  $1+3x+9x^2$  

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

•  $x+x^3+x^5$  

•  $x-x^3+x^5$  

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

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

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

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

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

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

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

Tags

CCSS.HSA.SSE.A.2

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

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

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

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

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

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.APR.A.1