Problem 1 Answer the following questions and explain your responses. You may use any type of calculator or other technology to perform any necessary calculations, but you must clearly state what you are computing, what you use to compute it, and what the result is. Examples of responses with sufficient explanations are below. • The area of a region is | sin(x²) dr Using Wolfram Alpha, I found that the area to 3 decimal places is .310. • I need to solve x* + 3x + 2x² +1= 0 to find the limits of integration. Using my TI83, I found that to 3 decimal places, x = -2.618, –.382. Incorrect answers and correct answers with incorrect or insufficient justification will not receive credit. 2n2 + 2" Suppose {an}n=1 and let s, = Σ then ak: A. ak. If it is known that sn = k=1 k=2 A converges to –1. (B) converges to 1. © converges to 0. D converges, but not to –1, 0, or 1. (E could converge or diverge. F diverges. Write the geometric series below in summation notation, then compute its value or explain why it diverges. В. (1) 2 (1) 3 (1)4 (1)
Problem 1 Answer the following questions and explain your responses. You may use any type of calculator or other technology to perform any necessary calculations, but you must clearly state what you are computing, what you use to compute it, and what the result is. Examples of responses with sufficient explanations are below. • The area of a region is | sin(x²) dr Using Wolfram Alpha, I found that the area to 3 decimal places is .310. • I need to solve x* + 3x + 2x² +1= 0 to find the limits of integration. Using my TI83, I found that to 3 decimal places, x = -2.618, –.382. Incorrect answers and correct answers with incorrect or insufficient justification will not receive credit. 2n2 + 2" Suppose {an}n=1 and let s, = Σ then ak: A. ak. If it is known that sn = k=1 k=2 A converges to –1. (B) converges to 1. © converges to 0. D converges, but not to –1, 0, or 1. (E could converge or diverge. F diverges. Write the geometric series below in summation notation, then compute its value or explain why it diverges. В. (1) 2 (1) 3 (1)4 (1)
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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Transcribed Image Text:Problem 1
Answer the following questions and explain your responses.
|You may use any type of calculator or other technology to perform any necessary calculations, but
you must clearly state what you are computing, what you use to compute it, and what the result is.
Examples of responses with sufficient explanations are below.
• The area of a region is
sin(x²) dx Using Wolfram Alpha, I found that the area to 3 decimal places is .310.
• I need to solve x* + 3x + 2x² + 1 = 0 to find the limits of integration. Using my TI83, I found that to 3
decimal places, x = -2.618, –.382.
Incorrect answers and correct answers with incorrect or insufficient justification will not receive credit.
Suppose {an}n=1 and let sn =
2n2.
Sak. If it is known that 8n =
+ 2"
, then )`,
A.
ak:
2n
k=1
k=2
A) converges to –1.
B) converges to 1.
C converges to 0.
D converges, but not to –1, 0, or 1.
(E could converge or diverge.
F diverges.
В.
Write the geometric series below in summation notation, then compute its value or explain why it
diverges.
3
4
(4)
2
+2
+ 2
+2
+...
(В) 12
C 8
(D
3
E 0
F It diverges
G None of these
18
Given that arctan(2r) = (-1)* . 2²k+1
2k +1
-x2k+1, the series (-1)k. 2²k+1
2k + 1
C.
-(x – 2)2k+1 is the Taylor
k=0
k=0
series centered at:
A) x = -2
B) x = 0
C) x = 2
for the function:
(A arctan(2x)
B arctan(2x – 2)
C arctan(2x – 4).
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