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The graph of a function g is shown in the figure. Use it to state the values (if theyEXAMPLE 7exist) of the following:lim g(x)(b)x 2+lim g(x)(c) im g(x)X » 2(a)X »2-3lim g(x)lim g(x)(f) m_g(x).X »5(d)(e)2SOLUTIONFrom the graph we see that the values of g(x) approachXas x1approaches 2 from the left, but they approach 1as x approaches 2 from the right.-224ThereforeVideo Example(b) m g(x) =x 2+(a) m g(x)and1=(c) Since the left and right limits are different, we conclude that the limit as x approaches 2 ofg(x) does not exist.The graph also shows that(e) m g(x) =(d) m g(x)andXx » 5+x » 5-(f) This time, the left and right limits are the same and so, by this theorem, we havelim g(x)X »5X=Despite this fact, notice that g(5)2

Question
The graph of a function g is shown in the figure. Use it to state the values (if they
EXAMPLE 7
exist) of the following:
lim g(x)
(b)
x 2+
lim g(x)
(c) im g(x)
X » 2
(a)
X »2-
3
lim g(x)
lim g(x)
(f) m_g(x).
X »5
(d)
(e)
2
SOLUTION
From the graph we see that the values of g(x) approach
Xas x
1
approaches 2 from the left, but they approach 1
as x approaches 2 from the right.
-2
2
4
Therefore
Video Example
(b) m g(x) =
x 2+
(a) m g(x)
and
1
=
(c) Since the left and right limits are different, we conclude that the limit as x approaches 2 of
g(x) does not exist.
The graph also shows that
(e) m g(x) =
(d) m g(x)
and
X
x » 5+
x » 5-
(f) This time, the left and right limits are the same and so, by this theorem, we have
lim g(x)
X »5
X
=
Despite this fact, notice that g(5)2
help_outline

Image Transcriptionclose

The graph of a function g is shown in the figure. Use it to state the values (if they EXAMPLE 7 exist) of the following: lim g(x) (b) x 2+ lim g(x) (c) im g(x) X » 2 (a) X »2- 3 lim g(x) lim g(x) (f) m_g(x). X »5 (d) (e) 2 SOLUTION From the graph we see that the values of g(x) approach Xas x 1 approaches 2 from the left, but they approach 1 as x approaches 2 from the right. -2 2 4 Therefore Video Example (b) m g(x) = x 2+ (a) m g(x) and 1 = (c) Since the left and right limits are different, we conclude that the limit as x approaches 2 of g(x) does not exist. The graph also shows that (e) m g(x) = (d) m g(x) and X x » 5+ x » 5- (f) This time, the left and right limits are the same and so, by this theorem, we have lim g(x) X »5 X = Despite this fact, notice that g(5)2

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check_circleAnswer
Step 1

Consider the given graph of th...

From the graph it is observed that as x approaches to 2 from left side the value of the function
g(x) is 4
Thus lim gx
x 2
4
=
(b)
From the graph it is observed that as x approaches to 2 from right side the value of the function
g(x) is 1
Thus lim g x1
x-2
(c)
Since, the left and right side of the limits are different the lim g(x)
x 2
does not exist
help_outline

Image Transcriptionclose

From the graph it is observed that as x approaches to 2 from left side the value of the function g(x) is 4 Thus lim gx x 2 4 = (b) From the graph it is observed that as x approaches to 2 from right side the value of the function g(x) is 1 Thus lim g x1 x-2 (c) Since, the left and right side of the limits are different the lim g(x) x 2 does not exist

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