January 7th, 2017, 02:44 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 09:42 AM. 
January 7th, 2017, 03:55 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,790 Thanks: 923 
$\displaystyle{\lim_{x \to 3}}~ 3 + m \dfrac{\sin(\pi x)}{x3} = 3  m \pi$ $\displaystyle{\lim_{x \to 3}}~ 1m x = 1  3m$ for what values of $m$ does $1  3 m = 3  m \pi$ ? 

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continuity, function 
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