MATHEMATICS 120 PROBLEM SET 2
Due September 18, 2002
For full credit, please show all work.
f 3 (x) − 9
1. (5 marks) We know that lim √
= 4. What is lim f (x)?
x→5
x→5
x−5
2. Find the following limits, or else explain why they do not exist:
√
√
2 + 3x + x2 − 2 − 3x + x2
(a) (5 marks) lim
,
x→0
x2
x3
x3 (b) (5 marks) lim
−
.
x→∞ x2 − 1
x2 + 1
3. (5 marks) If lim |f (x)| = 1, does the limit lim f (x) have to exist? If so, what is it?
x→3
x→3
What if lim |f (x)| = 0?
x→3
Please also read Sections 1.1–1.3 of the textbook and make sure that you can solve the
practice problems at the end of each section.
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