Ws 1.1 Limits And Continuity Worksheet With Answers - Pennsylvania 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
is continuous
f x
3
2
+
−
x
2
x
3
x
at the following. Justify.
x =
x =
x =
(a)
(b)
0
1
2
⎧ −
2
<
x
,
x
0
⎪
=
=
6. For
f x
( )
0.001,
x
0
, algebraically determine the following:
⎨
⎪
>
x
,
x
0
⎩
( )
( )
( )
( )
x = . Justify.
lim
f x
lim
f x
(a)
f
0
(b)
(c)
(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:
(
)
θ
x
85
45
11
=
=
−
+
−
+
=
(a)
lim sin
(b)
(c)
lim 2
lim 57
x
2
x
100
x
99999
x
5
π
11
→
x→
6
x
0
θ
→
6
8. Evaluate each of the following:
=
=
=
(a)
lim tan
x
(b)
lim tan
x
(c)
lim tan
x
−
+
π
π
π
→
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
Page 2 of 7
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