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1. Determine whether the following series converge or diverge with proof. a. e. k2)] b. Elvk-Vk-11* f. c. n sin(1/n) g. jkink n=1 d. I/-1 2. Determine of the following series converges conditionally or absolutely. 2"n! 5.8.11 (3n +2) 3. Determine of the following series converges conditionally or absolutely. n=l Power Series 1 4. Find McLaurin series for the function f defined by f(x) using two (1-x) different techniques. 5. Find a power series representation of the function f defined by 1 f(x) centered at a = 2. (1-x)4 6. Find the Taylor series for f(x)=In(2+ x) with center a =-1. Find the interval of convergence. 7. Find a power series representation and determine the interval of convergence y = sech x at a In(2). 8. Use a power series representation to calculate the following limits and integrals: sinx-x+fx tan x - x a. lim c. lim x->0 x5 x-0 b. (V1+rd d. ( arctan(x²) xx 9. Approximate fby a Taylor polynomial with degree n at the number a. Use Taylor's Inequality to estimate the accuracy of the approximation of f when x lies in the given interval. a. f(x) = In(1 + 2x), a = 1, n = 3, 0.5b. a 0, n = 3, 05x501

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Calculus Problems
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