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January 7th, 2017, 03:44 AM   #1
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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.
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January 7th, 2017, 04:55 AM   #2
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$\displaystyle{\lim_{x \to 3}}~ 3 + m \dfrac{\sin(\pi x)}{x-3} = 3 - m \pi$

$\displaystyle{\lim_{x \to 3}}~ 1-m x = 1 - 3m$

for what values of $m$ does

$1 - 3 m = 3 - m \pi$ ?
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