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 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: 7,502 Thanks: 2511 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: 19,887 Thanks: 1836 Where n is an odd integer. Thanks from v8archie
 November 25th, 2016, 05:55 AM #4 Newbie   Joined: Oct 2015 From: London Posts: 22 Thanks: 0

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