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AP EAMCET · Maths · Limits

\[
\lim _{x \rightarrow 0}\left(\frac{4^x-1}{2^x-1}-\frac{\sqrt{4+3 x}-2}{x}\right)=
\]

  1. A 0
  2. B \(\frac{5}{4}\)
  3. C \(\log 2-3\)
  4. D \(\frac{\log 4}{\log 2}-3\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{5}{4}\)

Step-by-step Solution

Detailed explanation

\( \lim _{x \rightarrow 0}\left(\frac{4^x-1}{2^x-1}-\frac{\sqrt{4+3 x}-2}{x}\right) \) \( = \lim _{x \rightarrow 0}\left(\frac{(2^x-1)(2^x+1)}{2^x-1}\right) - \lim _{x \rightarrow 0}\left(\frac{\sqrt{4+3 x}-2}{x}\right) \)…