find the limit

Question

lim┬(x→1)⁡〖(∛x-1)/(∜x-1)〗

Answer 1

lim_x→1{[x^1/3 - 1]/[x^1/4-1]}  (plugging in x=1 yields the indeterminate                                               form 0/0

 

Using L'Hopital's Rule, the given limit is equivalent to:

 

   lim_x→1{(1/3)x^-2/3/(1/4)x^-3/4} = (4/3)lim_x→1(x^1/12)

 

                                            = (4/3)(1) = 4/3

Answer 2

(x - 1)^1/3 / (x - 1)^1/4

(x - 1)^4/12 / (x - 1)^3/12

(x - 1)^1/12

 

Does that get you started?