# math homework

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all questions in file. there are 3 questions do them and show your work. please make sure to do them 100% correct because it quiz.

Math 133, Fall 2017 QUIZ 4 - Due Wednesday, December 6, 2017 Name: | {z Please print clearly Instructions: Be sure to show your work! No notes, books, or calculators may be used. 1. Determine the center, radius and interval of convergence of the power series: P∞ (2x−1)n (a) n=0 n 3n (b) n!(x+4)n n=0 10n (n+1) P∞ 1 } Math 133, Fall 2017 QUIZ 4 - Due Wednesday, December 6, 2017 2 2. Find the degree-2 Taylor polynomial T2 (x) of f (x) = ex centered at 1. 3. Find the Maclaurin series of the function f (x) = 2 3x 9 + x2 Math 133, Fall 2017 QUIZ 4 - Due Wednesday, December 6, 2017 Table of Maclaurin series ∞ X 1 = xn = 1 + x + x2 + x3 + · · · 1−x R=1 n=0 ex = ∞ X xn n=0 sin(x) = ∞ X (−1)n n=0 cos(x) = ∞ X tan (x) = ∞ X R=∞ x2n x2 x4 x6 =1− + − + ··· (2n)! 2! 4! 6! (−1)n n=0 x x2 x3 + + + ··· 1! 2! 3! x3 x5 x7 x2n+1 =x− + − + ··· (2n + 1)! 3! 5! 7! (−1)n n=0 −1 n! =1+ x2n+1 x3 x5 x7 =x− + − + ··· 2n + 1 3 5 7 3 R=∞ R=∞ R=1

pallveechem123
School: Rice University

here is solution; kindly speak to me if any doubt.

Question 1:

(2 x  1) n
n  3n

Tn  

Using Ratio Test,

Limit n

Tn 1
Tn

 imit n

(2 x  1) n 1
(n  1)3( n 1)
(2 x  1)
(n)3( n )

n

 imit n

(2 x  1)( n)
(n  1)3
1
2

2x  1
3

Radius of convergence is 1; and centre of convergence is  ,0 
For interval of convergence

2x  1  3
 3  2x  1  3
1  x  2
Check...

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Anonymous
Outstanding Job!!!!

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