1. ## 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.

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

2. ## Re: computing limit

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.

$\displaystyle \lim_{x \to 6} \frac{\frac{1}{6}-\frac{1}{x}}{6-x}$
start by getting a common denominator to combine the two fractions in the numerator

3. ## Re: computing limit

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

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

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

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

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

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

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

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

4. ## Re: computing limit

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

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

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

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

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

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

$\displaystyle = \lim_{x \to 6} \frac{1}{-6x} = -\frac {1}{36}$
fixed the next-to-last line