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The questions from exam 2 of math 106, sections d and e, covering topics such as series convergence, power series, and taylor series. Students are asked to determine if certain series converge or diverge, find the radius and interval of convergence of a power series, and expand functions like sin2θ and cos2θ using taylor series. The document also includes formulas for the derivatives and taylor series of cosh x and sinh x.
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Name Exam 2 Math 106, sections D and E March 20, 2003
(a)
n=
n^3 3 n^ (b)
n=
n + 1 n^2 + 1
n=
xn n(n + 1)(n + 2). For extra credit, find the exact value of the series.
x (^) + e−x 2 and^ sinh^ x^ =^
ex^ − e−x
(a) What is the derivative of cosh x? What is the derivative of sinh x? (b) Write down the Taylor series around zero of cosh x and sinh x. (c) Write down the first three nonzero terms of the Taylor series of f (x) = cos x cosh x around zero. (d) Try to write down the whole Taylor series of f (x) = cos x cosh x around zero.
