Problem #2: 00 What is the smallest number of terms of the series n2 2n that would have to be added in order to n=1 estimate its sum with an absolute error that is less than .0001? Problem #2: Just Save Submit Problem #2 for Grading Problem #2 Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark:Problem #1: Find a power series representation of the following function and determine the radius of convergence. f(x) = 4+ x 2 (A) ECIn An R = 21/3 (B) X(-1)2 x * 2n + 3 n= 0 An+ 1, R= 2 ( C) EG-1)+ 1x x 2n + 3 1=0 1=0 4n R =2 (D) (-1) 2 +122 +2 An+ 1, R=2 (E) (-In 1x2 +2 1= 0 4n + 1, R =21/3( ( F) E(-1 ) +1 12 +3 1= 0 An R = 21/3 ( G) _(-1 ) +2 4n R = 2 (H) n= 0 4n + 1, R = 21/3 n=0 Problem #1: Select v Just Save Submit Problem #1 for Grading Problem #1 Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark: Problem #2: Evaluate the following integral as a power series. In(1 + x 8) dx (A) (-1)" x9n + 7 8n +8 (n + 1)(9n + 7) (B) (n +1)(8n +8) (C) (D) ron to 1=0 n=( (9n + 1)(9n) (E) (1)" x8n +9 1=0 (n +1)(8n +9) 12= 0 (n +1)(8n +9) F) - on + 9 In + 7 (8n + 7) (8n) (G) - iM8 7= 0 (n + 1)(9n + 7 ) (H) (-1)2 x8n +8 1= 0 1= 0 (n +1)(8n +8) Problem #2: Select vProblem #3: Find the sum of the following series. (-1)" x 2n+ 1 42n+1 (2n + 1)! n=0 Problem #3: Enter your answer symbolically, as in these examples Just Save Submit Problem #3 for Grading Problem #3 Attempt # 1 Attempt #2 Attempt # 3 Your Answer Your Mark: Problem #4: Find the Taylor series for f (x) = - 2 centered at a = 2. (A) (1)" (n + 1 ) (1)" (n + 1 ) 2n+1 (x- 2)" (B) M 8 (1)"(n + 1 ) 2(x - 2)" (C) 2n+1 - (x - 2)" (D) M8 2n+1 2n+2 (x - 2)n 1=0 1=0 n=0 8 2n+1 ( x - 2 ) " ( F ) > (-1)n (n + 1) 2n+ 2 (x - 2)" (G) (1)n 2n ( x - 2 ) " ( H ) on (x- 2)1 1=0 n= 0 12= 0 n= 0 Problem #4: Select v Just Save Submit Problem #4 for Grading Problem #4 Attempt # 1 Attempt #2 Attempt #3 Your Answer: Your Mark:Problem #5: Find a simplified expression for ( -1/2 ). (A) (1) - 1 . 3 . 5 . ... . (2n -3) (B) (-1)" -12 . 4 . 6 . ... . (2n -2) (-1)" -13 . 5 . 7 . ... . (2n -1) 2" n! 212 -In! 212 -In! (D) ()"3 . 5 . 7 . ... . (2n -1) (ES (-1)"-1 . 3 . 5 . ... . (2n - 1) (1)"3 . 5 . 7 . ... . (2n -3) 2" n 2" n! 2" n! () ()2 . 4 . 6 .... . (2n -2) ()1 . 3 . 5 . ... . (2n -3) 2" n 2n -In! Problem #5: Select v Just Save Submit Problem #5 for Grading Problem #5 Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark: Problem #6: Let T2(x) be the 2nd degree Taylor polynomial for the function f(x) = 4 + re * centered at a = 0. Find T2(1). Problem #6: Just Save Submit Problem #6 for Grading Problem #6 Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark: Problem #7: Let f(x) = 2, 0.2