Question

Find the value of this limit:

Answer 1

tell me the question please

Answer 2

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

Answer 3

can u attach it with clear pls

Answer 4

attach it with what? @sudharsa

Answer 5

http://gyazo.com/9e646627ecf766a91ef117db60d3c64d

Answer 6

Hint: factor the numerator.

Answer 7

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

Answer 8

@across ?

Answer 9

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

Answer 10

dvide numerator and denominator by x^1/3 yeah

Answer 11

You don't have to divide, @sudharsa.

Answer 12

ok ur also goog idea that mke it simple

Answer 13

across is good then answer is simple yeah

Answer 14

but what is sqrt(x^2/3)

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

okay thank you.