Question
lim f x x X X Left hand limit atx x lim f x lim f x h X lim f x x X X
![image text in transcribed](https://s3.amazonaws.com/si.experts.images/answers/2024/06/665c516147205_177665c51613e81c.jpg)
lim f x x X X Left hand limit atx x lim f x lim f x h X lim f x x X X Continuity of Functions lim x h lim x h 2x h 20 x 0 0 RSITY OF DELE Since lim f x lim f x x Hence lim f x x Now the value of the function at x x is f x x from equation 1 and 2 we have lim f x f x x f x 0 Thus f x x is continuous at x x Since is an arbitrary element of R Therefore f x is continuous at each point of R Hence f x is continuous on R Example 4 Show that the function f x defined by Exfar if x 0 if x 0 is continuous on R Solution Given function is 1 xsin if x 0 X 0 if x 0 N
![image text in transcribed](https://s3.amazonaws.com/si.experts.images/answers/2024/06/665c516147205_177665c51613e81c.jpg)
lim f x x X X Left hand limit atx x lim f x lim f x h X lim f x x X X Continuity of Functions lim x h lim x h 2x h 20 x 0 0 RSITY OF DELE Since lim f x lim f x x Hence lim f x x Now the value of the function at x x is f x x from equation 1 and 2 we have lim f x f x x f x 0 Thus f x x is continuous at x x Since is an arbitrary element of R Therefore f x is continuous at each point of R Hence f x is continuous on R Example 4 Show that the function f x defined by Exfar if x 0 if x 0 is continuous on R Solution Given function is 1 xsin if x 0 X 0 if x 0 N
Step by Step Solution
There are 3 Steps involved in it
Step: 1
![blur-text-image](https://dsd5zvtm8ll6.cloudfront.net/includes/images/document_product_info/blur-text-image.webp)
Get Instant Access with AI-Powered Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
![blur-text-image](https://dsd5zvtm8ll6.cloudfront.net/includes/images/document_product_info/blur-subtext-image.webp)
Step: 3
![blur-text-image](https://dsd5zvtm8ll6.cloudfront.net/includes/images/document_product_info/blur-subtext-image.webp)
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started