(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the limit:

[tex]lim_{x \rightarrow 1} (2-x)^{tan \frac{\pi x}{2}}[/tex]

2. Relevant equations

3. The attempt at a solution

I first tried to find the limit of ln of the function inorder to turn the power into a multiplication and got:

[tex]lim_{x \rightarrow 1} \frac{ ln(2-x) sin \frac{\pi x}{2}}{cos \frac{\pi x}{2}}[/tex]

Then I used L'hopitals rule and got:

[tex]lim_{x \rightarrow 1} ln( (2-x)^{tan \frac{\pi x}{2}} ) = \pi / 2[/tex]

That means that [tex]lim_{x \rightarrow 1} (2-x)^{tan \frac{\pi x}{2}} = e^{\pi / 2}[/tex]

Is that right? I tried putting in values to my calc and it looks like the answer should be 1?

What did I do wrong?

Thanks.

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# Homework Help: A tricky limit

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