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NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Limits

NDA 2017 · Mathematics · Limits

What is _ x arrow 0 (e^x-(1+x))/(x^2) equal to?

What is lim⁡x→0ex−(1+x)x2\lim _{x \rightarrow 0} \frac{e^x-(1+x)}{x^2} equal to?

Options

  1. A0
  2. B1
  3. C1/2
  4. D2

Correct answer

B. 1

Step-by-step solution

lim⁡x→0ex−(1+x)x2\lim _{x \rightarrow 0} \frac{e^x-(1+x)}{x^2} If we keep x=0x=0, it is 00\frac{0}{0}. So, applying L'Hospital rule. lim⁡x→0ex−(1+x)x2=12lim⁡x→0ex−1x=12×1=12.\lim _{x \rightarrow 0} \frac{e^x-(1+x)}{x^2}=\frac{1}{2} \lim _{x \rightarrow 0} \frac{e^x-1}{x}=\frac{1}{2} \times 1=\frac{1}{2} .
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