AP EAMCET · Maths · Limits
\[
\lim _{x \rightarrow 0}\left(\frac{4^x-1}{2^x-1}-\frac{\sqrt{4+3 x}-2}{x}\right)=
\]
- A 0
- B \(\frac{5}{4}\)
- C \(\log 2-3\)
- D \(\frac{\log 4}{\log 2}-3\)
Answer & Solution
Correct Answer
(B) \(\frac{5}{4}\)
Step-by-step Solution
Detailed explanation
\( \lim _{x \rightarrow 0}\left(\frac{4^x-1}{2^x-1}-\frac{\sqrt{4+3 x}-2}{x}\right) \) \( = \lim _{x \rightarrow 0}\left(\frac{(2^x-1)(2^x+1)}{2^x-1}\right) - \lim _{x \rightarrow 0}\left(\frac{\sqrt{4+3 x}-2}{x}\right) \)…
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