Q228 / 270 · NDA 2020 · Mathematics

What is $\lim _{x \rightarrow 0} \frac{3^x+3^{-x}-2}{x}$ equal to?

  • Correct answer
    A
    0
  • B
    -1
  • C
    1
  • D
    Limit does not exist

Solution

$\lim _{x \rightarrow 0} \frac{3^x+3^{-x}-2}{x}=\lim _{x \rightarrow 0} \frac{3^x \cdot \log 3-3^{-x} \cdot \log 3}{1}$ (By L'Hospital rule) $=\frac{3^0 \cdot \log 3-3^0 \cdot \log 3}{1}=0$

Hence, the correct answer is option: 'A'.

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