Home › MCQs › SSC Pure Mathematics › Question #11154
Back to Questions
SSC Pure Mathematics QUESTION #11154
Question 1
$\displaystyle\lim_{x\to 1}\frac{x^2 - x}{1 - x + \ln x}$ is:
  • $2$
  • $-2$✔️
  • $1$
  • $-1$
Correct Answer Explanation
At $x=1$: numerator $= 1-1=0$, denominator $= 1-1+0=0$ (indeterminate $0/0$). Apply L'Hôpital's Rule: $\frac{2x-1}{-1+1/x}$. At $x=1$: $\frac{1}{0}$ — still indeterminate. Apply again: $\frac{2}{-1/x^2}$. At $x=1$: $\frac{2}{-1} = -2$.