18. One-sided and two-sided limits Use the graph of g in the figure to find the following values or state that they do not exist. If a limit does not exist, explain why. a. g(2) b. lim g(x) x-27 c. lim g(x) x→2+ d. lim g(x) e. g(3) f. lim g(x) x-3 g. lim g(x) 2-3+ h. g(4) i. lim g(x) x 4
18. One-sided and two-sided limits Use the graph of g in the figure to find the following values or state that they do not exist. If a limit does not exist, explain why. a. g(2) b. lim g(x) x-27 c. lim g(x) x→2+ d. lim g(x) e. g(3) f. lim g(x) x-3 g. lim g(x) 2-3+ h. g(4) i. lim g(x) x 4
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Transcribed Image Text:18. One-sided and two-sided limits Use the graph of g in the figure to find the following values or state that they do not
exist. If a limit does not exist, explain why.
in
a. g(2)
b. lim g(x)
x→2
e. g(3)
f. lim g(x)
x 3
g. lim g(x)
x→3+
c. lim g(x)
x→2+
y
d. lim g(x)
x→2
h. g(4)
i. lim g(x)
x 4
4
1
5
3
2
0
1
2
3
y = g(x)
4
5
X
Expert Solution
Step 1
a. In the graph , corresponding to x = 2 , the point y = 3 is darkened inside which means the point y = 3 is included .
And the point y = 2 is not darkened hence it is not included
So g (2) = 3
b. is the left limit of g at x= 2.
To the left of x = 2 the graph is a straight line. As x = 2 is approached from left clearly g approaches 2 (but not attained)
So = 2
c. is the right limit of g at x= 2.
To the right of x = 2 , g(x) is constant when x < 3
So = 3
d. Since 2 = = 3 , does not exists
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