Next: About this document ...
SAMPLE MIDTERM 1, MAT 141 10/11/99
- 1.
- The graph of a different the function f is given in
each of the figures below. For each graph
sketch the corresponding function g indicated below on the same axes.
For A,
g(x) = f(x)-2.
For B,
g(x) = f( x-3).
For C,
g(x) =-f(-x).
1#1
2#2
3#3
2#2
4#4
- 2.
- Place the letter corresponding to the correct answer in the box
next to each question.
- (a)
-
5#5
The equation of the line passing through (0,2) and (3,-1) is
(a)
6#6(b)
7#7(c)
8#8
(d)
9#9(e)
10#10
(f) none of these.
- (b)
-
5#5Suppose f and g are given by the following tables. What is f(g(2))?
x |
0 |
1 |
2 |
3 |
4 |
f(x) |
2 |
3 |
1 |
2 |
4 |
g(x) |
1 |
3 |
2 |
4 |
0 |
(a) 0
(b) 1(c) 2(d) 3(e) 4(f) it is undefined.
- (c)
-
5#5Suppose that for all B>0 there is a C>0 so that x > C implies
f(x) > B. Then
(a)
11#11(b)
12#12(c)
13#13(d)
14#14
(e)
15#15.
(f) none of these.
- (d)
-
5#5Consider the right triangle on the left below. What is
16#16?
(a)
17#17(b)
18#18(c)
19#19(d)
20#20(e)
21#21(f) none of these.
22#22
- (e)
-
5#5The derivative of xh(x2) is
(a)
1 + 2x h'(x2)
(b)
h'(x2) 2x(c)
2x + xh'(x2)(d)
xh(x2) + x2 h'(x)(e)
h(x2) + 2x2 h'(x)
(f) none of these.
- (f)
-
5#5
The derivative of
f(x) = x2 + x3 at x= 2 is
(a) 12(b) 13(c) 14(d) 15(e) 16(f) none of these.
- (g)
-
5#5The natural domain of
23#23is
(a) all real numbers
(b) x> 0(c) x< -5(d)
24#24
or 0 < x(e) 25#25
or x> 5(f) none of these.
- (h)
-
5#5Suppose
f(1) = 3.4 and
f(1.1) = 3.6. Then the best estimate for
f'(1) is
(a) 3.5
(b) 3.4
(c) 2.0
(d) 20
(e) .2
(f) .002
- (i)
-
5#5A ball dropped from rest takes 3 seconds to hit the ground. From what
height was it droped (in feet)?
(a) 48
(b) 90
(c) 144
(d) 256
(e) 288
(f) none of these
- (j)
-
5#5What is the limit of
26#26
as
27#27?
(a) 0(b) 28#28(c) 1 (d) 2(e) 29#29(f) the limit fails to exist
- 3.
- For each of the following functions, find the derivative function.
- (a)
-
x10 + x1/2
- (b)
- 30#30
- (c)
-
31#31
- (d)
- 32#32
- (e)
-
33#33
- 4.
- Prove by induction that
34#34.
- 5.
- What are the following limits (you do not need to
justify your answer),
35#35
Using these, the definition of derivative and addition law for cosines,
36#36
prove that
37#37.
- 6.
- Suppose f satisfies the following two conditions for all real
values of x and y.
- (a)
-
f(x+y) = f(x) f(y)
- (b)
-
f(x) = 1 + x g(x) where
38#38.
Show that f is differentiable at every point and that
f'(x) = f(x).
Next: About this document ...
Chris Bishop
1999-10-11