Math 1206
Common Final Exam
Spring 2014
Test Version: A
Instructions: Please enter your NAME, ID Number, Test Version, and your CRN on the opscan sheet.
The CRN should be written in the field labeled Class ID. Leave the Date, Instructor/Class, Test Name,
Time and Test ID fields blank. Darken the appropriate circles below your ID number, below Class ID and
beside Test Version. Use a number 2 pencil. Machine grading may ignore faintly marked circles.
Mark your answers to the test questions in rows 1 - 14 of the op scan sheet. Your score on this test will be
the number of correct answers. You have one hour to complete this portion of the exam. Turn in the op scan
sheet with your answers and the question sheets at the end of this part of the final exam.
Exam Policies: You may not use a book, notes, formula sheet, calculator or a computer. Giving or receiving
unauthorized aid is an Honor Code Violation.
Signature:
Name (printed):
Student ID #:
Z
0
1. Find f (x) if f (x) =
(A)
1
ln(x)
Z
e
2. Evaluate
1
(A) 4 ln(2)
3
√
x
2t
dt. Assume x > 1.
ln(t2 )
√
−2 x
(B)
ln(x)
√
2 x
ln(x)
(C)
−1
ln(x)
(D)
(C)
π
4
(D) π
4dx
x (1 + (ln x)2 )
(B) 4 ln(2e)
3. Find the area between the curves y = x2 − 2x and y = x.
(A) 4.5
(B) 2.5
(C) 12
(D) 22.5
4. In the xy-plane, a 3-g mass is at (1, 3), and a 2-g mass is at (2, 1). Determine where a 1-g mass should
be placed in order that the center of mass of the resulting system be at the origin.
(A) (−7, −11)
Z
5. Evaluate
(B) (−5, −7)
(C) (−5, −6)
x−2 ln(x) dx.
(A)
1
1
ln(x) − + C
2
x
x
1
1
(B) − ln(x) − + C
x
x
(C)
1
1
ln(x) + + C
x
x
(D) −
Z
9 − x2
6. Evaluate
(A)
1/2
2
1
ln(x) + 3 + C
3
x
x
dx.
x
3
3/2
(9 − x2 ) sin−1
+C
4
3
(C) 3x −
(D) (−4, −8)
x2
+C
2
(B)
3 −1 x sin
+C
2
3
(D)
x
9
1 √
x 9 − x2 + sin−1
+C
2
2
3
Z
7.
1
dx equals
−x−2
1 x−2
(A)
+C
2 x+1
x2
(C)
(B) ln |(x − 2)(x + 1)| + C
1 x − 2 ln
+C
3 x + 1
Z
(D)
1
2
ln |x − 2| + ln |x + 1| + C
3
3
3
|x − 2| dx.
8. Evaluate
−1
(A) 5
(B) −4
(C) 4
(D) 6
9. Let f (x) be a differentiable
√ function whose graph passes through the point (1, 4) and whose slope for
each x > 0 is given by 3 x. Find f (4).
(A) 1
(B) 6
(C) 18
(D) 20
10. Evaluate lim
x→0
(A) −1
Z
1 − cos x + x sin x
1 − cos x
(B) e3
∞
(C) 3
(D) Does not exist
(C) e
(D)
2
2xex dx.
11. Evaluate
−∞
(A) 0
(B)
1
2
Integral
diverges
12. A toy rocket is launched from the ground level (x = 0, y = 0) and due to the wind it falls some distance
away from the launch site. The trajectory of the rocket is described by the curve
y = 10x(4 − x2 ).
Determine the distance s covered by the rocket from the launch moment to the moment it hits the
ground.
Z 2p
Z 2p
3
2
(A) s =
(B)
1 − (40x − 10x ) dx
s=
1 + (40 − 30x2 )2 dx
0
(C) s =
Z
0
√2
3
p
1 + (40 −
(D) s =
30x2 ) dx
0
Z
√2
3
p
1 + (40x − 10x3 )2 dx
0
13. A region bounded by the curves
x2
and y = 5 − x2
4
is revolved around the line y = −1. Find the volume of the generated solid using disk-washer method.
2
2 #
Z 2"
Z 5 p
2
x
√ 2
2
4 − x2 −
(A) V = π
(B) V = π
−1
dx
5 − y − (2 y) dy
4
−2
−1
y=
Z
(C) V = π
0
5
2
p
√ 2
1 + 5 − y − (1 + 2 y) dy
Z
2
"
6−x
(D) V = π
−2
2 2
−
x2
+1
4
2 #
dx
14. An elevator weighs 1000 lbs and is suspended at the bottom end of a 200-foot cable. The cable weighs
5 lb/ft. An electric motor at the top of the elevator shaft winds 190 ft of cable to lift the elevator from
the ground floor to the top floor. Which integral represents the amount of work done by the electric
motor?
Z 190
(A) W = 190 · 2000 =
2000 dy
0
Z
190
(B) W = 190 · 1000 +
Z
190
5(200 − y) dy =
0
Z
(1000 + 5(200 − y)) dy
0
200
(C) W = 190 · 1000 +
Z
200
5(190 − y) dy =
10
Z
(D) W = 190 · 1000 +
190
Z
5y dy =
0
(1000 + 5(190 − y)) dy
10
190
(1000 + 5y) dy
0