Prof. Haiman
Math 1A—Calculus
Fall, 2006
First Midterm Exam Solutions
Name
Student ID Number
Section time and Instructor
You may use one sheet of notes. No other notes, books or calculators allowed. There are
10 questions, on front and back. Write answers on the exam and turn in only this paper.
Show enough work so that we can see how you arrived at your answers.
1. Write a formula for the function whose graph is shown. Assume the lines continue to
infinity outside the part of the graph shown here, and that their slopes are simple fractions.
x
y
f
(
x
) =

x
x <
1
,
(
x
+ 1)
/
2
x
≥
1
2. If
f
(
x
) = 2
x
,
g
(
x
) = 1
/x
, and
h
(
x
) =
x
+ 5, find
f
◦
g
◦
h
.
f
◦
g
◦
h
(
x
) =
2
x
+ 5
.
3. Which of the following are 11 functions?
(a)
f
(
x
) =
x
3
, for all real numbers
x
(b)
f
(
x
) =
x
4
, for all real numbers
x
(c)
f
(
x
) =
x
3
, for
x
≥
0
(d)
f
(
x
) =
x
4
, for
x
≥
0
All except (b).
4. Find the inverse function of
f
(
x
) = 3 sin(
x
+ (
π/
4)).
f

1
(
x
) = sin

1
(
x/
3)

π/
4.
5. Simplify 16
log
2
(
x
)
.
16
log
2
(
x
)
= 2
4 log
2
(
x
)
= 2
log
2
(
x
4
)
=
x
4
. Strictly speaking, this is valid only for
x >
0.
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 Fall '08
 WILKENING
 Calculus, Continuous function, Limit of a function, Midterm Exam Solutions

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