Q250 / 270 · NDA 2023 (Phase 1) · Mathematics

What is $\lim _{x \rightarrow 1} \frac{x^9-1}{x^3-1}$ equal to?

  • A
    $-1$
  • B
    $-3$
  • Correct answer
    C
    $3$
  • D
    Limit does not exist

Solution

$\lim _{x \rightarrow 1} \frac{x^9-1}{x^3-1}$ $\lim _{x \rightarrow 1} \frac{\left(x^3\right)^3-1}{x^3-1}=\lim _{x \rightarrow 1} \frac{\left(x^3-1\right)\left(x^6+x^3+1\right)}{x^3-1}$ $=\lim _{x \rightarrow 1} x^6+x^3+1=3$

Hence, the correct answer is option: 'C'.

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