Calculus 2 Exam 2 Review Problems and Solutions (Integral Applications, Series Tests, Taylor Series)

(0:00) Introduction
(0:59) Volume of a solid of revolution
(8:18) Volume of a solid whose cross sections are semicircles
(12:56) Mass and center of mass of thin rod given mass density
(19:25) Work done by a force to pump water out of a tank
(30:55) Discrete annuity present value and future value (accumulated value). Use geometric series.
(42:14) Integral test for series
(48:56) Ratio test for series
(52:53) p-series example
(54:18) Comparison test for series
(56:15) Alternating series test
(58:32) Divergence test (the terms do not approach zero)
(1:00:26) Taylor series for x^2*cos(x^2) and interval of convergence
(1:02:26) Taylor series for x^2*(1+x)^(1/3) and interval of convergence
(1:05:12) Taylor series for 5/(1+25x^2) and interval of convergence
(1:07:22) Taylor series for arctan(5x) and interval of convergence
(1:10:15) Alternating series error bound
(1:15:11) Present value random variable of a future payment based on a uniform lifetime random variable

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