baldymcgee6
  • baldymcgee6
Find the value of this limit:
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
tell me the question please
baldymcgee6
  • baldymcgee6
\[\lim_{x \rightarrow 8} \frac{ (x^\frac{ 2 }{ 3 } - 4) }{ (x^\frac{ 1 }{ 3 } - 2) }\]
anonymous
  • anonymous
can u attach it with clear pls

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baldymcgee6
  • baldymcgee6
attach it with what? @sudharsa
baldymcgee6
  • baldymcgee6
http://gyazo.com/9e646627ecf766a91ef117db60d3c64d
across
  • across
Hint: factor the numerator.
baldymcgee6
  • baldymcgee6
how do we factor it? what do we take out?
baldymcgee6
  • baldymcgee6
across
  • across
The numerator has the form \(a^2-b^2=(a+b)(a-b)\).
anonymous
  • anonymous
dvide numerator and denominator by x^1/3 yeah
across
  • across
You don't have to divide, @sudharsa.
anonymous
  • anonymous
ok ur also goog idea that mke it simple
anonymous
  • anonymous
across is good then answer is simple yeah
baldymcgee6
  • baldymcgee6
but what is sqrt(x^2/3)
anonymous
  • anonymous
if x= 8 then cubic root of it will be 2 then proceed yeah
baldymcgee6
  • baldymcgee6
@across I don't understand how to factor the numberator..
across
  • across
If you let \(u=x^{1/3}\), then your numerator will become \(u^2-4\). Can you factor that?
baldymcgee6
  • baldymcgee6
its x^(2/3), but nonetheless, (u+2)(u-2)
across
  • across
You have to let \(u=x^{1/3}\) because then \(u^2=x^{2/3}\)... now re-substitute and solve your exercise.
baldymcgee6
  • baldymcgee6
okay thank you.

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