2. Pure Mathematics 2

Series Approximations — Quiz

Test your understanding of series approximations with 5 practice questions.

Practice Questions

Question 1

Find the second-order Taylor polynomial $P_2(x)$ for $f(x)=\ln(x)$ about $a=2$ and use it to approximate $\ln(2.1)$.

Question 2

Which function is represented by the Maclaurin series $\displaystyle\sum_{n=0}^{\infty}\frac{x^{2n+1}}{2n+1}$ for $\lvert x\rvert<1$?

Question 3

What primarily determines the radius of convergence $R$ of a Taylor series of a function $f(x)$ about $x=a$?

Question 4

Use the binomial series up to the $x^2$ term to approximate $\sqrt{1.05}$. Which value is closest to your result?

Question 5

Find the fourth-order Maclaurin polynomial $P_4(x)$ for $f(x)=e^{x^2}$.