Ws 1.1 Limits And Continuity Worksheet With Answers - Pennsylvania State University

Calculus Maximus
WS 1.1: Limits & Continuity
Name_________________________________________ Date________________________ Period______
Worksheet 1.1—Limits & Continuity
Short Answer: Show all work. Unless stated otherwise, no calculator permitted.
( )
= . Is it possible for this statement
1. Explain in your own words what is meant by the equation
lim
f x
4
x
2
( )
( )
= ? Explain. What graphical manifestation would
x = ?
to be true and yet
f
2
5
f x have at
2
( )
Sketch a possible graph of
f x .
( )
( )
= and
= . What graphical manifestation
2. Explain what it means to say that
lim
f x
3
lim
f x
6
+
x
1
x
1
( )
( )
x = ? Sketch a possible graph of
would
f x have at
1
f x .
3. Explain the meaning of each of the following, then sketch a possible graph of a function exhibiting the
indicated behavior.
( )
( )
= ∞
= −∞ .
(a)
lim
f x
(b)
lim
g x
+
→−
x
2
→−
x
3
2
+ −
x
x
20
=
4. For
f x
( )
, algebraically determine the following:
2
x
16
( )
( )
( )
( )
lim
f x
lim
f x
(a)
f
4
(b)
(c)
(d)
lim
f x
+
x
4
x
4
x
4
( )
( )
( )
( )
(a)
lim
f x
(b)
lim
f x
(c)
lim
f x
(d)
lim
f x
→−
→−
x
4
x
1
x
1
x
0
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