Question

lim as x ->1: (x^3-1)/(x^2-1)

Answer 1

lim_(x->1) (x^3-1)/(x^2-1)
Indeterminate form of type 0/0. Applying L'Hospital's rule we have,
lim_(x->1) (-1+x^3)/(-1+x^2)
= lim_(x->1) (( d(-1+x^3))/( dx))/(( d(-1+x^2))/( dx)):
= lim_(x->1) (3 x)/2
Factor out constants:
= 3/2 (lim_(x->1) x)
The limit of x as x approaches 1 is 1:
= 3/2