**Unformatted text preview: **10/19/2017 Print Test PRINTABLE VERSION
Test 3 You scored 48 out of 48
Question 1 Your answer is CORRECT.
Give the form of the partial fraction decompostion for the following rational function.
3x + 1
x a) b) c) d) e) f) A B A − 2x x + 1 Bx + C
+ x − 2 A x B
+
x 2 2 + 1 C D + +
x − 2 A x + 1 B C +
x + 2 (x + 2) A B 2 +
x 2 + 1 C +
x 2 +
x − 2 x − x C +
x 3 +
x + 2 A x − 1 B
+ x + 2 (x − 1) 2 Question 2 Your answer is CORRECT.
Give the form of the partial fraction decompostion for the following rational function.
4x + 4
2 (x − 2) a) A
(x − 2) (x 2 + 2) Bx + C
2 +
x 2 + 2 1/6 10/19/2017 b) c) Print Test
A B x − 2 (x − 2) A 2 +
x B x − 2 (x − 2) A 2 + 2 Cx + D + d) 2 +
x 2 + 2 B (x − 2) e) Cx + + 2 x A 2 + 2 B
+ x − 2 (x − 2) C
2 +
x 2 + 2 Question 3 Your answer is CORRECT.
Which of the following represents a correct substitution used to compute: ∫ a) b) c) d) e) ∫ 4 tan(θ) dθ 2 ∫ (θ) sec(θ) dθ 4 tan 2 ∫ 16 tan 2 ∫ ∫ 2
‾ dx
√‾
x‾‾‾‾‾
− 16 16 cos (θ) sec(θ) dθ (θ) sin(θ) dθ 16 tan(θ) sec(θ) dθ Question 4 Your answer is CORRECT.
Suppose that the trigonometric substitution x
integral is = 2 tan θ is used to compute an integral and the answer to the 1
θ + sin θ + C
5 Finish the problem by rewriting the answer in terms of x . 2/6 10/19/2017 a) b) c) d) e) Print Test
1
x + sin x + C
5 1 −1 tan
5 1 −1 tan 1 −1 tan
5 1 (2) −1 tan
5 + x‾‾‾‾
− 4
‾
√‾ 2
‾‾‾‾‾
‾
√x
+ 4 + + C
x x
(2) x
+ + C
2
‾‾‾‾‾
‾
√x
+ 4 x
(2) + C x x
(2) 5 2 x x
+ + C
2 x‾‾‾‾
− 4
‾
√‾ Question 5 Your answer is CORRECT.
The graph of 1
f (x) = is given below: 3
‾
√‾
x‾‾‾‾
+ 2 8 If you use numeric integration to determine ∫ 1
dx 0 with , which of the following statements n = 8 3
‾‾‾‾‾
‾
√x
+ 2 are true? a) Of all of the methods we have learned, the best approximation of this integral would be given if the
midpoint method is used.
3/6 10/19/2017 b) Print Test Ln < Rn . 8 c)
d) Ln > ∫ 1
dx
3
‾‾‾‾‾
‾
√x
+ 2 0 Rn > Sn Question 6 Your answer is CORRECT.
Which of the following indeﬁnite integrals cannot be computed by any method we have studied thus far? a) b) c) d) e) 2 ∫ 5e dx x ∫ 2 5 xe x ∫ 6 xe x ∫ dx 2 x ∫ x 3x e dx dx 2 3 (e ) dx Question 7 Your answer is CORRECT.
This is a written question, worth 13 points. DO NOT place the problem code on the answer sheet. A
proctor will ﬁll this out after exam submission. Show all steps (work) on your answer sheet for full
credit.
Problem Code: 783
Given
4 ∫ x
dx 2 2 x‾‾‾‾
− 4
‾
√‾ Part a: (3 points) Explain why this integral is improper.
Part b: (10 points) Re-write the integral using proper limit notation then compute the integral. a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem. 4/6 10/19/2017 Print Test Question 8 Your answer is CORRECT.
This is a written question, worth 13 points. DO NOT place the problem code on the answer sheet. A
proctor will ﬁll this out after exam submission. Show all steps (work) on your answer sheet for full
credit.
Problem Code: 824
Compute: 2 ∫ 4 tan (x) sec (x) dx a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem. Question 9 Your answer is CORRECT.
This is a written question, worth 13 points. DO NOT place the problem code on the answer sheet. A
proctor will ﬁll this out after exam submission. Show all steps (work) on your answer sheet for full
credit.
Problem Code: 913
Compute ∫ 4 x ln(x) dx a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem. Question 10 Your answer is CORRECT.
This is a written question, worth 13 points. DO NOT place the problem code on the answer sheet. A
proctor will ﬁll this out after exam submission. Show all steps (work) on your answer sheet for full
credit.
Problem Code: 1056
Use partial fraction decomposition to determine
4x − 3
∫ dx
(x − 2) (x + 3) 5/6 10/19/2017 Print Test a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem. 6/6 ...

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