# computing limit

• Oct 18th 2011, 03:36 PM
raymac62
computing limit
I am not sure how to go about computing this limit. I know the answer is -1/36.
Though, I am having difficulties with the preliminary algebra and simplification so that I can make x = to 6.

$\lim_{x \to 6} \frac{\frac{1}{6}-\frac{1}{x}}{6-x}$
• Oct 18th 2011, 03:40 PM
skeeter
Re: computing limit
Quote:

Originally Posted by raymac62
I am not sure how to go about computing this limit. I know the answer is -1/36.
Though, I am having difficulties with the preliminary algebra and simplification so that I can make x = to 6.

$\lim_{x \to 6} \frac{\frac{1}{6}-\frac{1}{x}}{6-x}$

start by getting a common denominator to combine the two fractions in the numerator
• Oct 18th 2011, 03:59 PM
raymac62
Re: computing limit
I just figured it out before I checked this! Can't believe what I was missing. Thanks though.

$\lim_{x \to 6} \frac{\frac{1}{6}-\frac{1}{x}}{6-x}$

$= \lim_{x \to 6} \frac{\frac{x-6}{6x}}{6-x}$

$= \lim_{x \to 6} \frac{x-6}{6x(6-x)}$

$= \lim_{x \to 6} \frac{x-6}{36x - 6x^2}$

$= \lim_{x \to 6} \frac{x-6}{-6x(-6+x)}$

$= \lim_{x \to 6} \frac{1}{-6x}$

$= -\frac {1}{36}$
• Oct 18th 2011, 04:09 PM
skeeter
Re: computing limit
Quote:

Originally Posted by raymac62
I just figured it out before I checked this! Can't believe what I was missing. Thanks though.

$\lim_{x \to 6} \frac{\frac{1}{6}-\frac{1}{x}}{6-x}$

$= \lim_{x \to 6} \frac{\frac{x-6}{6x}}{6-x}$

$= \lim_{x \to 6} \frac{x-6}{6x(6-x)}$

$= \lim_{x \to 6} \frac{x-6}{36x - 6x^2}$

$= \lim_{x \to 6} \frac{x-6}{-6x(-6+x)}$

$= \lim_{x \to 6} \frac{1}{-6x} = -\frac {1}{36}$

fixed the next-to-last line