56) Which of the following statements are true? 1 а) 1+xl1dx = > (-1)" 11n + 1 n=0 c0.1 b) . 0.001 arctan(x²)dx < 3 15 7nº + 14n2 + 3 | c) The power series -x" has radius of convergence R = 1. n19 + 2n12 + 34n6 + 8` d) The power series > n" -2" has radius of convergence R= ;. n!* n=0 e) If f(k) (0) = 0 for all k = 0, 1, 2, 3, ..., then f(x) = 0 for all x E R. 57) Consider the following power series: 24x + 24x° + 24x° + ...)` 24x²n+1. n=1 Which of the following statements are true? a) The radius of convergence of the series is 24. b) The interval of convergence is (–1, 1). c) If f(x) = E 24x2n+1, then f"(0) = 144. n=1 d) f(}) = 16. e) i f(x) dx =-12 ln().
56) Which of the following statements are true? 1 а) 1+xl1dx = > (-1)" 11n + 1 n=0 c0.1 b) . 0.001 arctan(x²)dx < 3 15 7nº + 14n2 + 3 | c) The power series -x" has radius of convergence R = 1. n19 + 2n12 + 34n6 + 8` d) The power series > n" -2" has radius of convergence R= ;. n!* n=0 e) If f(k) (0) = 0 for all k = 0, 1, 2, 3, ..., then f(x) = 0 for all x E R. 57) Consider the following power series: 24x + 24x° + 24x° + ...)` 24x²n+1. n=1 Which of the following statements are true? a) The radius of convergence of the series is 24. b) The interval of convergence is (–1, 1). c) If f(x) = E 24x2n+1, then f"(0) = 144. n=1 d) f(}) = 16. e) i f(x) dx =-12 ln().
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Solve both 56 and 57 please
Transcribed Image Text:56) Which of the following statements are true?
+1
a) /
b)"
1
dx = (-1)"
8.
1+x11'
11n +1
n=0
r0.1
0.001
arctan(x?)dx <
3
n15 – 7n6 + 14n² + 3
|
c) The power series >)
-x" has radius of convergence R = 1.
n19 + 2n12 + 34n6 + 8
n=0
d) The power series >
has radius of convergence R= ;.
n!
n=0
e) If f(*) (0) = 0 for all k = 0, 1, 2, 3, ..., then f(x) = 0 for all x E R.
57) Consider the following power series:
24x + 24x° + 24x° + . ..
> 24.x2n+1
n=1
Which of the following statements are true?
a) The radius of convergence of the series is 24.
b) The interval of convergence is (–1, 1).
c) If f(x) = 24.x2n+1, then f"(0) = 144.
n=1
d) f(;) = 16.
e) Si f(æ) dx = –12 In(}).
-12 In().
|
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