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

2023
Views:

346

Pages:

1
Author:

Kieran Caldwell

Workshop #26 1. Determine the interval of convergence for each of the following series. (a) (b) ∞ X n=3 ∞ X n=1 xn 5n ln n n(x − 3)n n+1 2. (a) The sum of a certain geometric series is 34 . What might the series be? 5 (b) The sum of a certain geometric series is . What might the series be? 1 − 2x (c) Looking at the series you got from part 2b, let p4 (x) represent the polynomial you get if you remove all terms with degree greater than 4. What is p4 (x)? 5 . Graph f (x) and p4 (x) on the same screen of your calcu(d) Consider the function f (x) = 1 − 2x lator. On what interval would you say p4 (x) is a good approximation of f (x)? 1 . 1 + 3x (b) Use your series above, and your knowledge of calculus, to find a series whose sum is ln |1 + 3x|. 3. (a) Find a series whose sum is (c) Let p3 (x) be the polynomial you get if you remove all the terms from the above series with degree greater than 3. What is p3 (x). (d) Graph f (x) = ln |1 + 3x| and p3 (x) on the same screen of your calculator. On what interval would you say p3 (x) is a good approximation of f (x)? 4. Recall that the Maclaurin series for ex is as follows. ex = 1 + x + x2 x3 x4 + + + ··· 2! 3! 4! ex + e−x . 2 ex − e−x (b) Use your result from above to find the Maclaurin series for sinh x = . 2 (a) Use the Maclaurin series for ex to find the Maclaurin series for cosh x =