Question

1. \( \lim _{x \rightarrow 1} \frac{\sqrt[3]{x}+\sqrt{x}+x \sqrt{x}-3}{x^{3}-1} \)

Answer 1

at x = 1 it is 0/0 ( indeterminate form )

using LHopital rule 

Differentiation of Numerator = (1/3)x^(-2/3) + (1/2) x^(-1/2) + (3/2)x^(1/2) + 0

Differentiation of Denominator = 3x² + 0

Now apply limit  then

Numerator/Denominator  at x = 1 will be 

{ (1/3) + (1/2)  + (3/2)  }/{ 3 }  = 7/9