COMEDK · Maths · 16. Limits
The value of \(\lim _{x \rightarrow 0} \frac{5^{x}-5^{-x}}{2 x}=\)
- A \(2 \log 5\)
- B 1
- C 0
- D \(\log 5\)
Answer & Solution
Correct Answer
(D) \(\log 5\)
Step-by-step Solution
Detailed explanation
\(\lim _{x \rightarrow 0} \frac{5^{x}-5^{-x}}{2 x}=\lim _{x \rightarrow 0} \frac{5^{x} \log 5+5^{-x} \log 5}{2}\) (Applying L'Hospital rule) \(=\frac{\log 5+\log 5}{2}=\log 5\)
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