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## Homework Statement

[itex]\frac{Lim}{x-> \pi/4}[/itex] tan(x)[itex]^{tan(2x)}[/itex]

[itex]\frac{Lim}{x-> \pi/4}tan(2x) [/itex] does not exist.

However, Wolfram Alpha and my TI-89 say that [itex]\frac{Lim}{x-> \pi/4}[/itex] tan(x)[itex]^{tan(2x)}[/itex]does exist, and that it's [itex]\frac{1}{e}[/itex]

I submitted this answer (it's web based homework and calculators are allowed) and found it was correct. I still don't understand how though.

## Homework Equations

tan(2x) = [itex]\frac{2tan(x)}{1-tan^{2}(x)}[/itex]

## The Attempt at a Solution

I attempted to split it in to

[itex] \frac{sin(x)^{tan(2x)}}{cos(x)^{tan(2x)}} [/itex], and then use L'Hospital's rule, but I can't seem to get the tan(2x) to go away. Both appear to be indeterminate, but neither one is 0 at the same time, so it doesn't appear that I should be using L'Hopital's rule in this case. However, I can't see any other way to proceed.

Thanks in advance.