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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Limits

NDA 2013 · Mathematics · Limits

What is _ x arrow 2 (2-x)/(x^3-8) equal to?

What is lim⁡x→22−xx3−8\lim _{x \rightarrow 2} \frac{2-x}{x^3-8} equal to?

Options

  1. A18\frac{1}{8}
  2. B−18-\frac{1}{8}
  3. C112\frac{1}{12}
  4. D−112-\frac{1}{12}

Correct answer

D. −112-\frac{1}{12}

Step-by-step solution

lim⁡x→22−xx3−8\lim _{x \rightarrow 2} \frac{2-x}{x^3-8} This is in the 00\frac{0}{0} form, we use L'Hospital rule lim⁡x→2−13x2=−13(2)2=−112\lim _{x \rightarrow 2} \frac{-1}{3 x^2}=\frac{-1}{3(2)^2}=-\frac{1}{12}
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