My Math Forum Continuity of a function

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 January 7th, 2017, 03:44 AM #1 Newbie   Joined: Dec 2016 From: Netherlands Posts: 14 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)/(x-3)) 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: 594 Thanks: 318 $\displaystyle{\lim_{x \to 3}}~ 3 + m \dfrac{\sin(\pi x)}{x-3} = 3 - m \pi$ $\displaystyle{\lim_{x \to 3}}~ 1-m x = 1 - 3m$ for what values of $m$ does $1 - 3 m = 3 - m \pi$ ?

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