finding a limit using only algebra

• February 19th 2009, 03:05 PM
Yamahammer342
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.
• February 19th 2009, 03:15 PM
skeeter
Quote:

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.

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

divide every term by x ...

$\lim_{x \to \infty} \frac{\frac{1}{x}+12}{\frac{8}{x}-3} = \frac{12}{-3} = -4
$
• February 19th 2009, 03:19 PM
Plato
Quote:

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.

$\frac{{1 + 12x}}{{8 - 3x}} = \frac{{\frac{1}{x} + 12}}{{\frac{8}
{x} - 3}}$

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
$\frac{1}{x} \to 0\text{ as } x \to \infty$