Download 1A - Math TAMU

MATH 151, FALL SEMESTER 2011
COMMON EXAMINATION I - VERSION A
Name (print):
Instructor’s name:
Signature:
Section No:
Part 1 – Multiple Choice (12 questions, 4 points each, No Calculators)
Write your name, section number, and version letter (A) of the exam on the ScanTron form.
Mark your responses on the ScanTron form and on the exam itself
1.
Let v
a.
b.
c.
d.
e.
2.
2, 4 and w
2i
6j. Compute 1 v
2
w .
1
2
3
4
5
A ball whose weight is 50 Newtons hangs from
two wires, one at angle 23° from horizontal,
and the other at angle 37° from horizontal.
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 T 1 and T 2 ?
a.
|T 1 | cos 23°
|T 2 | cos 37°
0
b.
|T 1 | cos 23°
|T 2 | cos 37°
50 and
|T 1 | sin 23°
|T 2 | sin 37°
0
and
|T 1 | sin 23°
|T 2 | sin 37°
0
c. |T 1 | cos 23°
d.
|T 1 | cos 23°
e. |T 1 | cos 23°
3.
|T 2 | cos 37°
50
|T 1 | cos 37°
|T 2 | cos 37°
0
0
and |T 1 | sin 23°
and |T 2 | sin 23°
and
Find the angle between the vectors v
a.
b.
c.
d.
e.
|T 1 | sin 23°
1, 2 and w
|T 2 | sin 37°
|T 2 | sin 37°
|T 2 | sin 37°
50
50
50
3, 1 .
0°
30°
45°
60°
90°
1
4.
5.
Find the scalar projection (component) and vector projection of v
a.
scalar projection
b.
scalar projection
c.
scalar projection
d.
scalar projection
e.
scalar projection
x2
x2
x2
x2
x2
y
y
y
y
y
r
r
r
r
r
x
x
3x
3x
3x
t
t
t
t
t
Let f x
a.
vector projection
vector projection
vector projection
4i
3j.
64 i
48 j
169
169
64 i
48 j
169
169
64 i 48 j
25
25
64 i 48 j
25
25
64 i 48 j
25
25
1
t and y
t2
t.
2
2
1
4t, 2 3t
t, 4 2t
3 2t, 4 t
2 3t, 1 4t
2 3t, 1 4t
3
x 2 4 . Which of the following is true?
x 2 2
lim f x
and
x 2
b.
lim f x
c.
lim f x
and
lim f x
x 2
e.
None of these.
lim f x
x 2
and
x 2
d.
lim f x
x 2
x 2
2
vector projection
12j onto w
Find a vector equation for the line which contains the point 2, 1 and is parallel to 3, 4 .
a.
b.
c.
d.
e.
7.
vector projection
Find the Cartesian equation for the graph of the parametric curve x
a.
b.
c.
d.
e.
6.
16
13
16
13
16
5
16
5
16
5
5i
lim f x
x 2
and
lim f x
x 2
8.
9.
2
Compute lim 1 t
t 1 1
t
a. 1
b. 2
c. 3
d. 4
e. Does not exist
Which interval contains the unique real solution of the equation 2x 3
a.
b.
c.
d.
e.
b.
c.
d.
e.
d.
e.
xx
3x
3
0
1
2
1
2
12. Evaluate lim 2x
x
a.
b.
x
3x
3
1
2
3
c.
d.
e.
3x 2 2
?
x 2 x 2
1
3
y 3
y
2
1
y
2
None of the above
x 3
c.
0?
y
2
11. Evaluate lim 2x
a.
b.
2
2, 1
1, 0
0, 1
1, 2
2, 3
10. Which of the following is a horizontal asymptote of f x
a.
x2
2
3
Part 2 – Work Out Problems (5 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.
13. (10 points) An object is moving in the xy-plane and its position vector after t seconds is
rt
t
3, t 2
2t .
a.
Find the position vector of the object at time t
b.
Does the object pass through the point 1, 8 ? If yes, when? If no, why not?
c.
Does the object pass through the point 2, 20 ? If yes, when? If no, why not?
5.
5
14.
(14 points) Sketch the graph of the function
1 if
x
2
3
3
if
x
2
2
|x|
if
2
x
gx
4
x2
2 if
x
x
1
1
1
-3
-2
-1
1
-1
Then determine each of the following
-2
lim g x
x
2
lim g x
x
lim g x
lim g x
x 1
x 1
List all value(s) of x where g x is NOT differentiable:
4
g 2
2
g1
2
3
15. (9 points) Compute each of the following or prove the limit does not exist.
a.
lim
x 2
b.
lim
x 2
c.
lim
x 2
|x
x2
2|
2x
|x
x2
2|
2x
|x
x2
2|
2x
x2
16. (9 points) Consider f x
a.
x
2x 8
4
p
if x
4
if x
4
Find lim f x or explain why it does not exist.
x 4
b.
Find the value(s) of p that make f x continuous at x
exists.
17. (10 points) Consider the function f x
4 or explain why no such p
1.
x
a.
Find f x , the derivative of f x , using the limit definition of the derivative.
b.
Find the slope of the tangent line to the curve y
f x at x
3.
5
Name (print):
Question
Points/Max
1-12
/48
13
/10
14
/14
15
/9
16
/9
17
/10
Total
6
Section No:
/100