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NDA 2020
Exam
NDA
Year
2020
Subject
Mathematics
Chapter
Limits

NDA 2020 · Mathematics · Limits

What is _ x arrow 0 3^x+3^ -x -2 x equal to?

What is lim⁡x→03x+3−x−2x\lim _{x \rightarrow 0} \frac{3^x+3^{-x}-2}{x} equal to?

Options

  1. A0
  2. B-1
  3. C1
  4. DLimit does not exist

Correct answer

A. 0

Step-by-step solution

lim⁡x→03x+3−x−2x=lim⁡x→03x⋅log⁡3−3−x⋅log⁡31\lim _{x \rightarrow 0} \frac{3^x+3^{-x}-2}{x}=\lim _{x \rightarrow 0} \frac{3^x \cdot \log 3-3^{-x} \cdot \log 3}{1} (By L'Hospital rule) =30⋅log⁡3−30⋅log⁡31=0=\frac{3^0 \cdot \log 3-3^0 \cdot \log 3}{1}=0
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