Limits & Continuity Math Worksheet 1.1 - Portland State University Page 2
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7Calculus Maximus
WS 1.1: Limits & Continuity
2
x
x
5. Using the definition of continuity, determine whether the graph of
f x
is continuous
3
2
x
2
x
3
x
at the following. Justify.
x
x
x
(a)
0
(b)
1
(c)
2
2
x
,
x
0
6. For
f x
( )
0.001,
x
0
, algebraically determine the following:
x
,
x
0
x . Justify.
(a)
f
0
(b)
lim
f x
(c)
lim
f x
(d)
lim
f x
(e) continuity of f at
0
x
0
x
0
x
0
7. Evaluate each of the following continuous functions at the indicated x-value:
x
85
45
11
(a)
lim sin
(b)
(c)
lim 57
x
2
x
100
x
99999
x
5
lim 2
11
x
6
x
0
6
8. Evaluate each of the following:
(a)
lim tan
x
(b)
lim tan
x
(c)
lim tan
x
x
x
x
2
2
2
2
2
2
(d)
lim
(e)
lim
(f)
lim
x
5
x
5
x
5
x
5
x
5
x
5
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