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NDA 2012
Exam
NDA
Year
2012
Subject
Mathematics
Chapter
Limits

NDA 2012 · Mathematics · Limits

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

What is lim⁡x→−2(x+2x3+8)\lim _{x \rightarrow-2} \left(\frac{x+2}{x^3+8}\right) equal to?

Options

  1. A1/4
  2. B-1/4
  3. C1/12
  4. D-1/12

Correct answer

C. 1/12

Step-by-step solution

lim⁡x→−2x+2(x)3+(2)3lim⁡x→∞−2x+2(x+2)(x2−2x+4)=1(−2)2−2(−2)+4(C)=14+4+4=112.\begin{aligned} & \lim _{x \rightarrow-2} \frac{x+2}{(x)^3+(2)^3} \\ & \lim _{x \rightarrow \infty}-2 \frac{x+2}{(x+2)\left(x^2-2 x+4\right)} \\ & =\frac{1}{(-2)^2-2(-2)+4}(\mathrm{C}) \quad=\frac{1}{4+4+4}=\frac{1}{12}.\end{aligned}
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