y3.0EXAMPLE 7The graph of a function g is shown in the figure. Use it to statethe values (if they exist) of the following:2.5(a)X → 2-lim g(x)lim g(x)(c) lim g(x)(b)2.0X → 2+X → 21.5(d) lim g(x)lim g(x)(f) lim_ g(x)·X →(e)X → 5-*5 9(x).1.0X → 5+0.5SOLUTIONFrom the graph we see that the values of g(x) approachasx approaches 2 from the left, but they approachas x approaches 2 from-224the right. ThereforeVideo Example )(a) lim g(x) =X → 2-(b) lim g(x) =andX → 2+(c) Since the left and right limits are different, we conclude that the limit as Xapproaches 2 of g(x) does not exist.The graph also shows that(d) lim g(x) =X → 5-(e) lim g(x) =X → 5+and(f) This time, the left and right limits are the same and so, by this theorem,we havelim_ g(x)=X → 5Despite this fact, notice that g(5) # 1.

EXAMPLE 7 The graph of a function g is shown in the figure. Use it to state 3.0 the values (if they exist) of the following: 2.5 (a) lim g(x) (b) lim g(x) (c) lim g(x) 2.0 X - 2- X → 2+ x- 2 1.5 (d) lim g(x) (e) lim g(x) (f) lim X- 5- X - 5+ 1.0 SOLUTION From the graph we see that the values of g(x) approach as 0.5 x approaches 2 from the left, but they approach as x approaches 2 from х -2 4 6 the right. Therefore Video Example (a) lim g(x) = X - 2- (b) lim g(x) and X- 2+ (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 (d) lim g(x) = x - 5- (e) lim g(x) = X - 5+ and (f) This time, the left and right limits are the same and so, by this theorem, we have lim X - 5 m g(x) Despite this fact, notice that g(5) # 1.

EXAMPLE 7 The graph of a function g is shown in the figure. Use it to state 3.0 the values (if they exist) of the following: 2.5 (a) lim g(x) (b) lim g(x) (c) lim g(x) 2.0 X - 2- X → 2+ x- 2 1.5 (d) lim g(x) (e) lim g(x) (f) lim X- 5- X - 5+ 1.0 SOLUTION From the graph we see that the values of g(x) approach as 0.5 x approaches 2 from the left, but they approach as x approaches 2 from х -2 4 6 the right. Therefore Video Example (a) lim g(x) = X - 2- (b) lim g(x) and X- 2+ (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 (d) lim g(x) = x - 5- (e) lim g(x) = X - 5+ and (f) This time, the left and right limits are the same and so, by this theorem, we have lim X - 5 m g(x) Despite this fact, notice that g(5) # 1.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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