(12 pts) Use trigonometric substitution to evaluate the integral
(12 pts) Use trigonometric integrals to evaluate the integral
(12pts) Use the integral test to determine whether the series converges or diverges. [Assume the 3 conditions for this test are satisfied, NO need to prove them]
(12 pts) Find the Maclaurin series for. [Assume that has a power series expansion. Also find the associated radius of convergence. [HINT: use Substitution method by using the series expansion from the Cheat Sheet]. SHOW WORK by expressing your answer as a power series and as a polynomial with minimum 5 terms.
(12 pts) Use power series to evaluate the limit.
[HINT: use the series expansion from the Cheat Sheet]. SHOW WORK by expressing your answer as a power series and as a polynomial with minimum 5 terms.
(12 pts) Evaluate the indefinite integral using power series.
[HINT: use the series expansion from the Cheat Sheet]. SHOW WORK by expressing your answer as a power series and as a polynomial with minimum 5 terms.
(14 pts) Find the radius of convergence and interval of convergence of the series . [either apply the Ratio or Root Test]
(14pts)
Find the volume of the solid generated by rotating the region bounded by the equations
Sketch the region, the solid, and a typical disk or washer.
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