Let f (x) = 1/x sin 1/x , for x not = 0.– Let xn = 1/n π^2. What is limn→∞ xn? limn→∞ sin( 1/xn )? limn→∞ f (xn)? Justify.– Is f continuous at 0? Justify.– In the definition of f (x) above, f (x) is not assigned a value at x = 0. Redefine f (x)as follows: f (x) = 1/x sin 1/x , for x is not equal to 0 and f (0) = 0. Is f (x) continuous at 0? Why?– Can f be redefined at 0 so that it’s continuous on R? Justify

Let f (x) = 1/x sin 1/x , for x not = 0.– Let xn = 1/n π^2. What is limn→∞ xn? limn→∞ sin( 1/xn )? limn→∞ f (xn)? Justify.– Is f continuous at 0? Justify.– In the definition of f (x) above, f (x) is not assigned a value at x = 0. Redefine f (x)as follows: f (x) = 1/x sin 1/x , for x is not equal to 0 and f (0) = 0. Is f (x) continuous at 0? Why?– Can f be redefined at 0 so that it’s continuous on R? Justify

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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