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November 24th, 2016, 08:04 PM   #1
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Function Continuous

Is a function defined at this point continuous?

L'Hôpital's rule ?
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November 24th, 2016, 08:17 PM   #2
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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.
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November 24th, 2016, 08:41 PM   #3
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Where n is an odd integer.
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November 25th, 2016, 05:55 AM   #4
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