1. ## Finding Limit

Im trying to find the limit on the following problem
LIM(x->infinity) $\displaystyle (1/2x - 4/x^2)$
Generally I find limits when there division so im kinda stuck on this.

2. $\displaystyle \lim_{x \to \infty}\left( \frac{1}{2x} - \frac{4}{x^2}\right)=0$

3. Originally Posted by Spec
$\displaystyle \lim_{x \to \infty}\left( \frac{1}{2x} - \frac{4}{x^2}\right)=0$
Thanks for the help, Can you explain why?

4. Originally Posted by Red350z
Thanks for the help, Can you explain why?
If you let $\displaystyle x = \frac{1}{t}$ then your problem becomes

$\displaystyle \lim_{t \to 0} \;\frac{1}{2}t - 4 t^2$

5. Alright so make it 1/t makes the limit zero, so the problem comes out zero, but in the original it was the lim approaching infinity.
Im not good with this at all, so youll have to hold my hand through it.

6. Think of it this way; as you make $\displaystyle x$ larger and larger, the denominator gets larger and larger, and if the denominator is getting larger and larger then the fraction is approaching 0.

With danny's substitution, if $\displaystyle x$ is approaching infinity, then $\displaystyle t$ much approach 0, because if you make the denominator of a fraction smaller and smaller (essentially, as you make the denominator closer and closer to zero), the whole fraction gets larger and larger.

7. OH! Okay got it, thanks for the help everyone! i think i repped you all or thanked which ever it is.