Ws 1.1 Limits And Continuity Worksheet With Answers - Pennsylvania State University Page 5
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7Calculus Maximus
WS 1.1: Limits & Continuity
14. (Calculator permitted) Fill in the table for the following function, then use the numerical evidence (
to 3 decimal places) to evaluate the indicated limit. (Be sure you’re in radian mode)
( )
sin 3x
( )
=
f x
x
−
−
−
x
0.1
0.01
0.001
0
0.001
0.01
0.1
( )
f x
( )
=
Based on the numeric evidence above,
lim
f x
→
x
0
Multiple Choice: Put the Capital Letter of the correct answer in the blank to the left of the number. Be
sure to show any work/analysis.
⎛
⎞
1
−
=
_____ 15.
lim 1
⎜
⎟
⎝
x
⎠
−
→
x
0
(C) −∞
(E) ∞
(A) 1
(B) 2
(D) 0
−
≠
⎧
3
x x
,
1
( )
( )
= ⎨
_____ 16. Find
lim
f x
if
f x
=
1,
x
1
→
⎩
x
1
3
(A) 2
(B) 1
(C)
(D) 0
(E) DNE
2
( )
_____ 17. For which of the following does
lim
f x
exist?
→
x
4
I.
II.
III.
( )
( )
( )
graph of
graph of
f x
graph of
f x
f x
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
< ≤
⎧
ln ,
x
0
x
2
( )
( )
= ⎨
_____ 18. If
, then
lim
f x
is
f x
2
< ≤
x
ln 2, 2
x
4
→
x
2
⎩
(A) ln 2
(B) ln 8
(C) ln16
(D) 4
(E) nonexistent
Page 5 of 7
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