MHT CET · Maths · Limits
\(\lim _{x \rightarrow 0}\left(\frac{3^{x}-1}{x}\right)\) is equal to
- A \(2 \log 3\)
- B \(3 \log 3\)
- C \(\log 3\)
- D None of these
Answer & Solution
Correct Answer
(C) \(\log 3\)
Step-by-step Solution
Detailed explanation
\(\lim _{x \rightarrow 0}\left(\frac{3^{x}-1}{x}\right) \quad\left(\frac{0}{0}\right.\) form \()\)
Using L' Hospital's rule, \(=\lim _{x \rightarrow 0} \frac{3^{x} \log 3-0}{1}=3^{0} \log 3\)
Using L' Hospital's rule, \(=\lim _{x \rightarrow 0} \frac{3^{x} \log 3-0}{1}=3^{0} \log 3\)
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