## anonymous 3 years ago Find the value of this limit:

1. anonymous

2. anonymous

$\lim_{x \rightarrow 8} \frac{ (x^\frac{ 2 }{ 3 } - 4) }{ (x^\frac{ 1 }{ 3 } - 2) }$

3. anonymous

can u attach it with clear pls

4. anonymous

attach it with what? @sudharsa

5. anonymous
6. across

Hint: factor the numerator.

7. anonymous

how do we factor it? what do we take out?

8. anonymous

@across ?

9. across

The numerator has the form $$a^2-b^2=(a+b)(a-b)$$.

10. anonymous

dvide numerator and denominator by x^1/3 yeah

11. across

You don't have to divide, @sudharsa.

12. anonymous

ok ur also goog idea that mke it simple

13. anonymous

across is good then answer is simple yeah

14. anonymous

but what is sqrt(x^2/3)

15. anonymous

if x= 8 then cubic root of it will be 2 then proceed yeah

16. anonymous

@across I don't understand how to factor the numberator..

17. across

If you let $$u=x^{1/3}$$, then your numerator will become $$u^2-4$$. Can you factor that?

18. anonymous

its x^(2/3), but nonetheless, (u+2)(u-2)

19. across

You have to let $$u=x^{1/3}$$ because then $$u^2=x^{2/3}$$... now re-substitute and solve your exercise.

20. anonymous

okay thank you.

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