Could someone please show me how to workout problems of these types:
Find the limit. (If you need to use - or , enter -INFINITY or INFINITY.)
Thanks in advance!
Oh, i did a little mistake. I've corrected it. Now that it's correct, with that factor, you can eliminate the root. See what happens:
$\displaystyle \lim_{x\to\infty}\sqrt{36x^2+x}-6x \cdot \frac{\sqrt{36x^2+x}+6x}{\sqrt{36x^2+x}+6x}=\lim_{ x\to\infty}\frac{x}{\sqrt{36x^2+x}+6x}=\lim_{x\to\ infty}\frac{1}{\sqrt{36+\frac{1}{x}}+6} $
Now you can conclude.
How did you go from $\displaystyle
=\lim_{x\to\infty}\frac{x}{\sqrt{36x^2+x}+6x}=\lim _{x\to\infty}\frac{1}{\sqrt{36+\frac{1}{x}}+6}
$
[/tex]?? It looks like in some places you multiplied out by $\displaystyle \frac{1}{x}$ and other parts you multiplied out by $\displaystyle \frac{1}{x^2}$