Unit 4B Practice Exam A

Find the radius and interval of $\sum (x-1)^n/[n2^n]$.

Find a series for $1/(4-x)$.

Differentiate $\sum x^n$ and identify its sum.

Find the degree-four Maclaurin polynomial for $e^x$.

Write the first four nonzero terms of $\sin x$.

Derive the series for $\ln(1+x)$.

Find the first four terms of $e^{-x^2}$.

Use three nonzero terms to approximate $\cos(0.4)$.

Give an alternating-series error bound for the approximation.

Use Taylor's theorem to bound the error in approximating $e^{0.5}$ with $P_3$.

Approximate $\int_0^{0.5}e^{-x^2}dx$ using three integrated terms.

State why a Taylor series need not equal its source function automatically.