Use L'H to solve the limit as x approaches 2 of (x/2)^(1/(x-2))

Question

anonymous · Answer

This was taking a bit of time to calculate the derivative so I used Wolfram Alpha and it says the answer would be root e. Sorry I couldn't help more

anonymous · Answer

I need to show the steps, is there any way you could show me those? I got the same thing with wolfram.

anonymous · Answer

Wait, you can actually take out 1/2 from x/2 because it is a constant and just evaluate x^(1/(x-2)). Now you would just treat it as you would as if you were finding the derivative of a^x, just it would be a bit more complicated because you would need to rewrite it.

anonymous · Answer

I know when I first took calculus one of the problems we were given was to find the derivative of x^x. This would be like that just it would be x^(1/(x-2)).

anonymous · Answer

Rewriting the problem would give us$$.5 e ^{(1/(x-2))\ln x}$$ Then you would just use the product rule to solve.

mertsj · Answer

$$\lim\frac{f(x)}{g(x)}=\lim \frac{f'(x)}{g'(x)}$$