Find lim (x^2-25)/(x^3-27) x- 3 ? Please help?? (:

Question

Find lim (x^2-25)/(x^3-27) x-> 3 ? Please help?? (:

ybarrap · Answer

ok, so what do you think we can do with this?

anonymous · Answer

graph it! :p lol

ybarrap · Answer

When I see this equation, I think that the top looks familiar, there is an x^2 term and a 25 term, which is 5^2. I also see that it is a difference of squares, which I know how to rewrite. Do you know how to rewrite this?

anonymous · Answer

no :o

ybarrap · Answer

Ok, so $a^2-b^2=(a+b)(a-b)$. This is very useful to remember. What is a and b in our case?

ybarrap · Answer

You can read this later: http://en.wikipedia.org/wiki/Difference_of_squares We have for our case $a=x$ and $b=5$. Next, let's look at the denominator: It's a difference of cubes: $\Large a^3-b^3$. There is also a formula for that. What is a and b in this case?

ybarrap · Answer

http://en.wikipedia.org/wiki/Difference_between_two_cubes#Sum.2Fdifference_of_two_cubes

ybarrap · Answer

You can read that later. We have now for this difference of cubes $\Large x^3-3^3$, which can be written as $(x-3)(x^2+3x+9)$.

ybarrap · Answer

So, no you have a factored numerator and denominator. In the denominator you have a term $x-3$. What happens as $x\to3$?

ybarrap · Answer

*now