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Math 1A Midterm 1 2005929 11:0012:30pm.
You are allowed 1 sheet of notes. Calculators are not allowed. Each question is worth
3 marks, which will only be given for a clear and correct answer.
1. Find the domain of the function
g
(
u
) =
√
u
+
√
2

u
.
2. Sketch the graph of
y
=

x
2

2
x

.
3. Find a formula for the inverse of the function
f
(
x
) = 1 +
e
x
3
.
4. Sketch the graph of a function
f
that satisﬁes the conditions
lim
x
→
0

f
(
x
) = 1
,
lim
x
→
0
+
f
(
x
) =

1
,
lim
x
→
1

f
(
x
) = 1
,
lim
x
→
1
+
f
(
x
) =

1
, f
(2) = 1
.
5. Evaluate the limit
lim
x
→
1
x
3

1
x
2

1
6. How close to 2 do we have to take
x
so that 5
x
+ 3 is within a distance of 0.01 from
13?
7. Find the numbers at which
f
is discontinuous, where
f
is deﬁned by
f
(
x
) =
x
2
if
x
≤
1,
f
(
x
) = 1
/x
if 1
< x <
3,
f
(
x
) = 1
/
2 +
√
x

3 if
x
≥
3.
8. What is
lim
x
→∞
(3
x
+ 1)(4
x
+ 1)
(
x
+ 1)(2
x
+ 1)
9. A curve has equation
y
=
f
(
x
). Write an expression for the slope of the secant line
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This note was uploaded on 03/08/2010 for the course MATH 1A taught by Professor Wilkening during the Fall '08 term at Berkeley.
 Fall '08
 WILKENING
 Math

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