I need to simplify and solve. Could u plz gimme a step by step answer bcuz i get very confused in these type of cubed root questions.

 

lim ((x+27)^1/3) -3) / x

x->0

 

Its x+27 all under a cubed root subtract 3, all of this divided by x.

 

Thanks in advance

Well, you could evaluate whats in the limit for successively smaller values of x, thereby determining the limit. That's the brute-force method.

 

There is another, more 'mathematical' method, which is basically multiplying the top and bottom by the conjugate of the top. So multiply the entire thing by

[math]

((x+27)^{1/3}+3)

[/math]

 

on the top and bottom. Then factor out any common factors, and substitute 0 for x and solve.

 

Cheers,

LF