January 7th, 2017, 03:44 AM  #1 
Newbie Joined: Dec 2016 From: Netherlands Posts: 15 Thanks: 0  Continuity of a function
I need to find out for which m the following function is continuous: g(x) = 3 + m*(sin(πx)/(x3)) if x < 3 and g(x)=1 − mx if x ≥ 3. The only examples I can find on determining the continuity of a function is compare the two functions around the point x=3 and determine which m makes them equal, but in this example the function for x < 3 will get an m that is infinitely small, as you will be going to sin(πx)/0 which will be infinitely big; how can I solve this otherwise? Last edited by skipjack; January 7th, 2017 at 10:42 AM. 
January 7th, 2017, 04:55 AM  #2 
Senior Member Joined: Sep 2015 From: CA Posts: 1,201 Thanks: 613 
$\displaystyle{\lim_{x \to 3}}~ 3 + m \dfrac{\sin(\pi x)}{x3} = 3  m \pi$ $\displaystyle{\lim_{x \to 3}}~ 1m x = 1  3m$ for what values of $m$ does $1  3 m = 3  m \pi$ ? 

Tags 
continuity, function 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Continuity of a function.  condemath2  Calculus  6  June 6th, 2014 12:19 PM 
prove continuity of function  frankpupu  Calculus  4  May 12th, 2012 08:21 AM 
Check the continuity of function  ladak  Real Analysis  1  October 21st, 2011 08:59 AM 
Continuity of a 2 variables function  jollysa87  Calculus  1  July 15th, 2009 06:58 PM 
Function Continuity  Tear_Grant  Calculus  2  April 19th, 2009 04:43 AM 