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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Limits

NDA 2021 · Mathematics · Limits

If a differentiable function f(x) satisfies _ x arrow-1...

If a differentiable function f(x)f(x) satisfies lim⁡x→−1f(x)+1x2−1=−32\lim _{x \rightarrow-1} \frac{f(x)+1}{x^2-1}=-\frac{3}{2} then what is lim⁡x→−1f(x)\lim _{x \rightarrow-1} f(x) equal to?

Options

  1. A−32-\frac{3}{2}
  2. B−1-1
  3. C00
  4. D11

Correct answer

A. −32-\frac{3}{2}

Step-by-step solution

lim⁡x→−1f(x)+1x2−1=−32[f′(x)2x]=−32\begin{aligned} & \lim _{x \rightarrow-1} \frac{f(x)+1}{x^2-1}=\frac{-3}{2} \\ & {\left[\frac{f^{\prime}(x)}{2 x}\right]=\frac{-3}{2}}\end{aligned} On integrating both sides, f(x)=−32x2+c where c= Constant lim⁡x→−1f(x)=lim⁡x→−1[−32x2+c]=−32\begin{aligned} & f(x)=\frac{-3}{2} x^2+c \quad \text{ where } c=\text{ Constant } \\ & \lim _{x \rightarrow-1} f(x)=\lim _{x \rightarrow-1}\left[\frac{-3}{2} x^2+c\right]=\frac{-3}{2}\end{aligned}
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