computing limit

**raymac62** · October 18th 2011, 03:36 PM

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.

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

**skeeter** · October 18th 2011, 03:40 PM

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

**raymac62** · October 18th 2011, 03:59 PM

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

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

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

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

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

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

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

$= -\frac {1}{36}$

**skeeter** · October 18th 2011, 04:09 PM

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

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