Question

36 and 38Steps and explaination please

Answer 1

Answer:

36.   Limit = 2/3.

Step-by-step explanation:

36.

(∛ x- 1)  / (√x - 1)

Rationalise the expression:-

Multiply top and bottom by (√x + 1):-

(∛x - 1)(√x + 1) /  (√x - 1)(√x + 1)

=  x^5/6  + ∛x - √x - 1 /  (x - 1)

Applying L'hopital's rule ( differentiating top and bottom of the fraction) we have:

Limit as x ----> 1 of  [5/6 x^-1/6 + 1/3 x^(-2/3)  - 1/2x^-1/2] / 1

= 5/6(1) + 1/3(1) - 1/2(1)  =  2/3  (answer).