University:
San Diego State University
Course:
MATH 151 | Calculus II
Academic year:

2023
Views:

243

Pages:

1
Author:

Joaquin Spears

Workshop #24 1. Determine whether the following series converge absolutely, converge conditionally, or diverge. (a) ∞ X √ (−1)n n=2 (b) n+1 n2 − 1 ∞ X (−1)n ln n n=3 n2 ∞ X (−1)n (c) n + ln n (e) (f) ∞ X (−n)n n=2 2n ∞ X (−1)n n=1 (g) n=2 (d) ∞ X (−1)n √ 3 n ln n n=2 ∞ X √ n (−1) √ 3 n=1 (h) ∞ X 2n + 3n n! + 2n (−1)n n=1 n2 + 3 n5 + 2n + 1 n + 2n √ 2n n2 + 2n 2. Let p(x) = a0 + a1 x +√a2 x2 + a3 x3 represent a cubic polynomial that we choose in order to closely approximate f (x) = x + 4. Suppose we do this by requiring that p(0) = f (0), p0 (0) = f 0 (0), p00 (0) = f 00 (0), and p000 (0) = f 000 (0). (a) What must a0 , a1 , a2 , a3 equal? (b) Now that you’ve found the polynomial p(x), graph it and f (x) on the same screen of your calculator to see how closely p approximates f . On what interval would you say p is a a good approximation of f ?