Question

$\underset{x\to 1}{Lim}\left(\frac{1}{1-x}-\frac{3}{1-x^3}\right)=$

• A. $1$
• B. $-1$
• C. $\frac{1}{2}$
• D. $-\frac{1}{2}$

Answer 1

The correct option is B $-1$

The question is of the form,
${lim}_{x\to 1}\frac{1+x+x^2-3}{1-x^3}$
Since the function is of $\frac{0}{0}$ form,
Using L-Hospital's rule
$={lim}_{x\to 1}\frac{2x+1}{-3x^2}$
$=-1$