anonymous
  • anonymous
Find lim (x^2-25)/(x^3-27) x-> 3 ? Please help?? (:
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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ybarrap
  • ybarrap
ok, so what do you think we can do with this?
anonymous
  • anonymous
graph it! :p lol
ybarrap
  • ybarrap
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?

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anonymous
  • anonymous
no :o
ybarrap
  • ybarrap
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
  • ybarrap
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
  • ybarrap
http://en.wikipedia.org/wiki/Difference_between_two_cubes#Sum.2Fdifference_of_two_cubes
ybarrap
  • ybarrap
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
  • ybarrap
So, no you have a factored numerator and denominator. In the denominator you have a term \(x-3\). What happens as \(x\to3\)?
ybarrap
  • ybarrap
*now

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