Solutions to Practic Midterm 1
You will find below some questions that are representative of the material we have covered
in Chapter 2.
These questions are
not
comprehensive, though.
You are responsible for
everything in Chapter 1 and 2 (although there won’t be any questions that directly cover
Chapter 1).
This exam is longer than an actual 50minute midterm. If you are timing yourself, a reasonable
exam may consist of problems 1,2,4,6,8,9. Another exam may consist of 3,4,5,6,7,8,10.
1
Find the points of discontinuity for the function
f
(
x
) =
√
16

x
2
1

cos
x
Solution
(
∞
,

4)
∪
[0
,
0]
∪
(4
,
∞
).
(alternate ok answer: for 4
<

x

or
x
= 2
πk, k
an integer.)
On this problem you should show a bit of work, ie that you are solving 16

x
2
<
0 and
1

cos
x
= 0.
2
lim
x
→
2
2
3(
x

2)
2
=
∞
lim
t
→
1
t

1
√
4
t

2
= lim
t
→
1
(
t

1)(
√
4
t
+ 2)
(
√
4
t

2)(
√
4
t
+ 2)
= lim
t
→
1
(
t

1)(
√
4
t
+ 2)
4(
t

1)
= 1
.
lim
t
→∞
t

1
√
4
t

2
= lim
t
→∞
t

1
√
4
t

2
1
/
√
t
1
/
√
t
= lim
t
→∞
√
t

1
/
√
t
√
4

2
/
√
t
=
∞
.
3
Find the following limits or explain why they do not exist.
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 Fall '07
 Osserman
 Calculus, lim, Continuous function, Limit of a function

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