# Thread: finding a limit using only algebra

1. ## finding a limit using only algebra

Use algebra to find the Limit as X approaches infinity of (1+12x) / (8-3x)

not being able to use the properties of limits and such, I have no clue where to even start.

2. Originally Posted by Yamahammer342
Use algebra to find the Limit as X approaches infinity of (1+12x) / (8-3x)

not being able to use the properties of limits and such, I have no clue where to even start.
$\displaystyle \lim_{x \to \infty} \frac{1+12x}{8-3x} =$

divide every term by x ...

$\displaystyle \lim_{x \to \infty} \frac{\frac{1}{x}+12}{\frac{8}{x}-3} = \frac{12}{-3} = -4$

3. Originally Posted by Yamahammer342
Use algebra to find the Limit as X approaches infinity of (1+12x) / (8-3x) not being able to use the properties of limits and such, I have no clue where to even start.
$\displaystyle \frac{{1 + 12x}}{{8 - 3x}} = \frac{{\frac{1}{x} + 12}}{{\frac{8} {x} - 3}}$
That is all the algebra there is to it.
Now I have no idea what you are expected to do other than to realize that
$\displaystyle \frac{1}{x} \to 0\text{ as } x \to \infty$