Question

\[\lim_{r \rightarrow 9} (r)^{1/2} / (r-9)^4 \]

I need a hint. Also, how do I write out a fraction through modifying the above code?

Answer 1

to rewrite as a fraction write the word "over" where you have the division symbol. If you have letters touching the word in the code you need a space between.
e.g.
{x^2over y^2}\[{x^2\over y^2}\]so yours is

lim_{r \rightarrow 9}{r^{1/2}\over (r-9)^4}\[\lim_{r \rightarrow 9}{r^{1/2}\over (r-9)^4}\]I have no tip yet though...

Answer 2

If you substitute \(r=9\) in \(\large \frac{r^{\frac{1}{2}}}{(r-9)^4}\), you get \(\large \frac{3}{0}\). This is enough to tell you that the limit goes to either to \(-\infty \text{ or }\infty\). But you can see that \(\frac{r^{\frac{1}{2}}}{(r-9)^{4}}\) is positive as you approach \(9\) from the left and from the right. So \(\large \lim_{r \rightarrow 9}{r^{1/2}\over (r-9)^4}=\infty.\)

Answer 3

Nice...and to think I've been writing out \frac{x^2}{y^2} all the time :) Good tip.

Answer 4

Really? I never knew that you could assume that if the numerator is a finite value and the denominator is zero, you could say its approaching infinity. Thank you.

Answer 5

lim_{r \rightarrow 9}{r^{1/2}\over (r-9)^4}

Answer 6

lim_{r \rightarrow 9}{r^{1/2}\over (r-9)^4}
highlight above and click "equation"
\[\lim_{r \rightarrow 9}{r^{1/2}\over (r-9)^4} \]

Answer 7

That's right @QRAwarrior, except the case when it is \(\large \frac{0}{0}\).