Q93 / 150 · MHT CET 2012 · Mathematics

$\lim _{x \rightarrow 0}\left(\frac{3^{x}-1}{x}\right)$ is equal to

  • A
    $2 \log 3$
  • B
    $3 \log 3$
  • Correct answer
    C
    $\log 3$
  • D
    None of these

Solution

$\lim _{x \rightarrow 0}\left(\frac{3^{x}-1}{x}\right) \quad\left(\frac{0}{0}\right.$ form $)$ Using L' Hospital's rule, $=\lim _{x \rightarrow 0} \frac{3^{x} \log 3-0}{1}=3^{0} \log 3$

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

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