November 24th, 2016, 08:04 PM  #1 
Newbie Joined: Oct 2015 From: London Posts: 22 Thanks: 0  Function Continuous
Is a function defined at this point continuous? L'Hôpital's rule ? 
November 24th, 2016, 08:17 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,599 Thanks: 2587 Math Focus: Mainly analysis and algebra 
No. 1) The function $\sin{(y)}$ is continuous for all $y$, so $\sin{(x\sin x)}$ is continuous wherever $x\sin x$ is continuous. What does that mean? 2) $\tan y$ is not continuous at $y=n\frac{\pi}2$. So $\tan \left(\frac{\pi}4 \cos(\sin x^\frac13)\right)$ is not continuous if $\frac{\pi}4 \cos(\sin x^\frac13)=n\frac{\pi}2$. For what values of $x$ is $\frac{\pi}4 \cos(\sin x^\frac13)=n\frac{\pi}2$? $\tan y$ is not continuous everywhere else so $\tan \left(\frac{\pi}4 \cos(\sin x^\frac13)\right)$ as long as $\frac{\pi}4 \cos(\sin x^\frac13)$ is continuous (and not equal to $n\frac{\pi}2$). Is there anywhere where $\frac{\pi}4 \cos(\sin x^\frac13)$ is not continuous? Last edited by skipjack; November 24th, 2016 at 08:35 PM. 
November 24th, 2016, 08:41 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,271 Thanks: 1959 
Where n is an odd integer.

November 25th, 2016, 05:55 AM  #4 
Newbie Joined: Oct 2015 From: London Posts: 22 Thanks: 0  

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