41. f(3) exists but lim, a f(x) does not. 42. f(-2) exists, lim,-2* f(x) = f(-2), but lim,-2f(x) does not exist. 43. f(4) exists, lim 4ƒ(x) exists, but f is not continuous at x = 4. 44. f(x) is continuous for all x except x = 1, where fhas a nonremov- able discontinuity.

41. f(3) exists but lim, a f(x) does not. 42. f(-2) exists, lim,-2* f(x) = f(-2), but lim,-2f(x) does not exist. 43. f(4) exists, lim 4ƒ(x) exists, but f is not continuous at x = 4. 44. f(x) is continuous for all x except x = 1, where fhas a nonremov- able discontinuity.

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...

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Question

In Exercises 41–44, sketch a possible graph for a function f that has
the stated properties.

41. f(3) exists but lim, a f(x) does not.
42. f(-2) exists, lim,-2* f(x) = f(-2), but lim,-2f(x) does not
exist.
43. f(4) exists, lim 4ƒ(x) exists, but f is not continuous at x = 4.
44. f(x) is continuous for all x except x = 1, where fhas a nonremov-
able discontinuity.

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