Ws 1.1 Limits And Continuity Worksheet With Answers - Pennsylvania State University Page 4
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7Calculus Maximus
WS 1.1: Limits & Continuity
1
( )
f x =
11. (Calculator Permitted) Sketch the graph of the function
in the space below, then
1
+
1 2
x
evaluate each, if it exists. If it does not exist, explain why. Name the type and location of any
discontinuity.
( )
( )
( )
( )
=
=
=
(a)
lim
f x
(b)
lim
f x
(c)
lim
f x
(d)
f
0
=
−
+
→
x
0
→
→
x
0
x
0
12. Using the definition of continuity at a point, discuss the continuity of the following function. Justify.
⎧ −
< −
2
x
,
x
1
⎪ ⎪
( )
=
− ≤ <
f x
x
,
1
x
1
⎨
⎪
(
)
2
−
≥
x
1 ,
x
1
⎪ ⎩
⎧
3ax − b,
x < 1
⎪
( )
( )
=
x = 1
is continuous at x = 1 . Show
13. For f x
5,
, find the values of a and b such that f x
⎨
⎪
2a x + b, x > 1
⎩
the work that leads to your answer.
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