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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Limits

NDA 2023 · Mathematics · Limits

What is _ x arrow 1 (x^9-1)/(x^3-1) equal to?

What is lim⁡x→1x9−1x3−1\lim _{x \rightarrow 1} \frac{x^9-1}{x^3-1} equal to?

Options

  1. A−1-1
  2. B−3-3
  3. C33
  4. DLimit does not exist

Correct answer

C. 33

Step-by-step solution

lim⁡x→1x9−1x3−1lim⁡x→1(x3)3−1x3−1=lim⁡x→1(x3−1)(x6+x3+1)x3−1=lim⁡x→1x6+x3+1=3\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
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