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Name (print):
Instructor: Yasskin
1-14
/56
Signature:
Section: 537,538,539
15
/10
MATH 151, Fall 2013
16
/10
FINAL EXAMINATION
17
/30
Part 1 – Multiple Choice (14 questions, 4 points each, No Calculators)
Total
/106
Write your name and section number on the ScanTron form.
Mark your responses on the ScanTron form and on the exam itself
1.
A ball whose weight is F
50 Newtons hangs from
two wires, one at angle 30° above horizontal on the left,
and the other at angle 60° above horizontal on the right.
Let T 1 be the tension in the first wire, and T 2 be the
tension in the second wire. Which set of equations can
be used to solve for
a.
b.
c.
d.
e.
2.
3
1 T2
T1
2
2
3
1 T1
T2
2
2
3
1 T2
T1
2
2
3
1 T1
T2
2
2
3
1 T1
T2
2
2
and
T1
0
0
0
0
0
T2 ?
3
1 T1
T2
2
2
3
1 T2
T1
2
2
3
1 T1
T2
2
2
3
1 T2
T1
2
2
3
1 T2
T1
2
2
Find the cosine of the angle between the vectors A
a.
cos
b.
cos
c.
cos
d.
cos
e.
cos
50
50
50
50
50
3, 4
and B
12, 5
56
65
4
65
16
65
4
65
56
65
1
3.
Evaluate lim
x
a.
b.
c.
d.
e.
4.
4x 3
5
x
8
4
2
0
b.
c.
d.
e.
2x
4
2, 1
1, 0
0, 1
1, 2
x
ln x
2014! x 2015
2016! x 2017
2015! x 2016
2016! x 2017
2015! x 2016
Find the line tangent to the curve y 3
a.
2
x4
5
Find the 2017-th derivative of f x
a.
b.
c.
d.
e.
6.
4x 3
Which interval contains the unique real solution of the equation x 3
a.
b.
c.
d.
5.
x4
4
5
3
5
3
5
4
5
2
x2
xy at
x, y
2, 2 . Its y-intercept is
7.
Near x
2, the graph of f x
x
2
1/5
has the shape:
b.
a.
c.
d.
e None of these
8.
lim x sin x
x 0 cos x
1
a.
b.
c.
d.
e.
9.
2
1
0
1
2
Water is poured onto a tabletop at dV
3 cm 3 / sec in such a way that it forms a circular
dt
puddle of radius r and constant height of h 0. 2 cm. Find the rate that the radius is
increasing when it is r 5 cm.
HINT: The puddle is actually a cylinder. What is its volume?
a.
b.
1
2
2
3
c.
d.
e.
3
2
2
10. Find the points of inflection of the function f x
a.
b.
c.
d.
e.
x
x
x
x
x
1 x5
20
1 x4.
3
0 and x 4 only
4 only
0 only
2 and x 2 only
4 and x 0 only
3
11. If the initial position and velocity of a car are x 0
at
a.
b.
c.
d.
e.
sin t
7
3
6
7
3
12. If A z
a.
b.
c.
d.
e.
6t find its position at t
1.
is the area under the parabola y
2
x 2 between x
2
x 2 between x
1 and x
z find A 3 .
4
21
24
27
30
36
1 x 2 between x
Right Riemann Sum with 3 equal intervals and right endpoints.
4
1 and x
6
8
9
11
13
14. Approximate the area under the parabola y
a.
b.
c.
d.
e.
2 and its accereration is
sin 1
cos 1
sin 1
sin 1
cos 1
13. Find the area under the parabola y
a.
b.
c.
d.
e.
3 and v 0
38
76
86
120
172
1 and x
7 using a
Part 2 – Work Out Problems (3 questions. Points indicated. No Calculators)
Solve each problem in the space provided. Show all your work neatly and concisely, and
indicate your final answer clearly. You will be graded, not merely on the final answer, but also on
the quality and correctness of the work leading up to it.
15. (10 points) Let f x
xe x and g x
f
1
x
the inverse function of f x . Find g e .
W
16.
(10 points) A rectangular field is surrounded by a fence and
divided into 3 pens by 2 additional fences parallel to one side.
If the total area is 50 m 2 find the minimum total length of fence.
L
5
17. (30 points) Analyze the graph of the function f x
or nowhere or undefined, say so.
6
a.
y-intercepts:
b.
x-intercepts:
c.
horizontal asymptote as x
:
d.
horizontal asymptote as x
:
e.
vertical asymptotes:
f.
first derivative:
f x
g.
critical points:
h.
intervals where increasing:
i.
intervals where decreasing:
j.
local maxima x and y coordinates :
k.
local minima x and y coordinates :
2
xe 2x . Find each of the following. If none
l.
Roughly graph the function:
1
y
-4
-3
-2
-1
1
2
3
4
x
-1
m. second derivative:
f
x
n.
inflection points x coordinate only :
o.
intervals where concave up:
p.
intervals where concave down:
7