Please help to answer the following limit:

Question

Answer: __ / __

Answer 1

Lim [x->1] {x^(1/3) - 1} / {x^(1/4) - 1}

Let x = u^12, then the limit becomes,

Lim [u->1] {u^4 -1} / {u^3 - 1}

(u^4 - 1) can be writtten as (u^2 - 1)(u^2 + 1) = (u - 1)(u + 1)(u^2 + 1)

(u^3 - 1) can be written as (u - 1)(u^2 + u + 1)

The limit now becomes,

Lim [u -> 1] (u - 1)(u + 1)(u^2 + 1)​ / (u - 1)(u^2 + u + 1)

Lim [u -> 1] (u + 1)(u^2 + 1)​ / (u^2 + u + 1)

As u -> 1, Lim -> 2*2 / 3 = 4/3

Limit = 4/3

Comments

Thank you!