Easy- Limit

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October 2nd 2012, 04:21 AM
Greymalkin

Easy- Limit

$\lim_{x\to\0}\frac{x}{\frac{1}{6}+\frac{1}{x-6}}$ I keep getting 36(36), actual answer is-36.

I get $\frac{x(6(x-6))}{\frac{6+x-6}{6(x-6)}}$ which equals $(6(x-6))(6(x-6))$

What have I done wrong?
October 2nd 2012, 06:03 AM
Plato

Re: Easy- Limit

Quote:

Originally Posted by Greymalkin

$\lim_{x\to\0}\frac{x}{\frac{1}{6}+\frac{1}{x-6}}$ I keep getting 36(36), actual answer is-36.
I get $\frac{x(6(x-6))}{\frac{6+x-6}{6(x-6)}}$ which equals $(6(x-6))(6(x-6))$

$\frac{x}{\frac{1}{6}+\frac{1}{x-6}}=\frac{6x(x-6)}{x}=6x-36$

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