Calculus II
Calculus II _______________
MAC2312 Spring 2001 Exam III name
No Calculator Portion **********************************************
1.) Does [pic] converge absolutely, conditionally or diverge? Why?
2.) Find the interval of convergence for [pic], that is the set of all x values for which the series converges.
3.) Find the sum of [pic] .
4.) Use the MacLauren Series for [pic] to find the MacLaurin series for [pic].
5.)a.) State the defining formula for the MacLaurin Series of f(x).
b.) Use this to find the first three nonzero terms in the MacLauren Series for [pic].
6.) Use logarithms and l’Hospital’s Rule as required to determine whether the sequence converges and find the limit if it does.
a.)[pic] b.)[pic]
Calculus II
MAC2312 Spring 2001 Exam III page 2
Calculator Portion **********************************************
7.) Use a TI-89/92 command to find the first four nonzero terms in the Taylor Series for y = sin x about x = π/8.
8.) a.) State the defining formula for the MacLaurin Series of f(x).
b.) Use the defining formula to find the first four nonzero terms in the MacLaurin Series for [pic]. Be sure to tabulate all appropriate derivative values.
c.) Use the above result to determine the first four nonzero terms in the MacLauren Series for [pic]
d.) Use a TI-89/92 comamand to determine the first four nonzero terms in the MacLauren Series for [pic].
9.a.) Use the first three nonzero terms in the Maclaurin series approximation of the integrand in [pic] to obtain an estimate of the integral value.
b.) Use the alternating series estimation theorem to estimate the error in part a.).
10.) Find the 15th partial sum for [pic] and document the procedure used.
E.C.) Find a power series solution of the differential equation [pic]
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