anonymous
  • anonymous
Use L'H to solve the limit as x approaches 2 of (x/2)^(1/(x-2))
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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anonymous
  • anonymous
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
  • anonymous
I need to show the steps, is there any way you could show me those? I got the same thing with wolfram.
anonymous
  • anonymous
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.

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anonymous
  • anonymous
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
  • anonymous
Rewriting the problem would give us\[.5 e ^{(1/(x-2))\ln x}\] Then you would just use the product rule to solve.
Mertsj
  • Mertsj
\[\lim\frac{f(x)}{g(x)}=\lim \frac{f'(x)}{g'(x)}\]

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