Question

Evaluate Lim x˄3-3x˄2+3x-1/x˄3-x
x͢ 1

Answer 1

it is (x-1)^3/x^3-x
So, reduced to (x-1)^2/x.
substituting 1, the answer is zero.

Answer 2

\[\lim_{x \rightarrow 1} \frac{x^{3}-3x^2+3x-1}{x^3-x}=\lim_{x \rightarrow 1} \frac{(x-1)^3}{x(x^2-1)}\]
\[=\lim_{x \rightarrow 1} \frac{(x-1)^3}{x(x+1)(x-1)}=\lim_{x \rightarrow 1} \frac{(x-1)^2}{x(x+1)}\]
Applying limit we find:
\[=\frac{(1-1)^2}{1(1+1)}=\frac{0}{2}=0\]
Thus the limit of the given function is 0