[SOLVED] Vv156 Honors Calculus II Assignment 7

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Exercise 7.1 [Ste10, p. 720] Use integral test to determine whether the series is convergent or divergent

Exercise 7.2 ([Ste10, p. 727] For what values of p ∈ R does the series converge?

Exercise 7.3  [Ste10, p. 727] Show that if a ≥ 0 and ^Xa_n < ∞, then.

Exercise 7.4 Work out the details of using Shanks transformation to calculate S^◦3(S₃) of the series

Exercise 7.5  [Ste10, p. 737] Determine whether the series is absolutely convergent, conditionally convergent, or divergent.

Exercise 7.6 [Ste10, p. 745]

Exercise 7.7  [Ste10, p. 751] Express the function as the sum of a power series by first using partial fractions. Find the interval of convergence.

Exercise 7.8  [Ste10, p. 752] Find a power series representation for the function and determine the radius of convergence.

(i) f(x) = ln(5 − x)                        (ii) f(x) = x² arctan(x³)

Exercise 7.9 [Ste10, p. 765] Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion.] Also find the associated radius of convergence.

(i) f(x) = x ³ −2. (ii) f(x) = 1/x, a = −3. (iii) f(x) = sinx, a = π/2. (iv) f(x) = √x, a = 16. − x , a =

Exercise 7.10  Find general solution x(t) to the following ODE’s

(i) x¨ + 4x˙ + 5x = e^5t + te^−2t cost                                                       (ii) x¨ + 4x˙ + 4x = t²e^−2t