Unit 4B Practice Exam B

Find the interval of convergence of $\sum n(x+2)^n/5^n$.

Find a power series for $x^2/(1-x)$.

Use the geometric series to derive $1/(1+x)^2$.

Find the Taylor polynomial of degree three for $\ln x$ at $a=1$.

Write the Maclaurin series for $\arctan x$.

Use the binomial series to approximate $\sqrt{1.02}$.

Determine how many sine-series terms guarantee error below $10^{-8}$ at $x=0.5$.

Approximate $\int_0^{0.25}\cos(x^2)dx$ with three nonzero terms.

Use power series to solve $y'=y$, $y(0)=2$.

Explain how uniform convergence differs from pointwise convergence.

Give a physics example where a Taylor approximation linearizes a model.

State a complete error argument for one approximation above.