TS EAMCET · Maths · Limits
\(\lim _{x \rightarrow 0} \frac{\sqrt{1+x^2}-\sqrt{1-x+x^2}}{3^x-1}\) is equal to
- A \(\frac{1}{\log _e 3}\)
- B \(\log _e 9\)
- C \(\frac{1}{\log _e 9}\)
- D \(\log _e 3\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{\log _e 9}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \lim _{x \rightarrow 0} \frac{\sqrt{1+x^2}-\sqrt{1-x+x^2}}{3^x-1} \\ & =\lim _{x \rightarrow 0} \frac{\sqrt{1+x^2}-\sqrt{1-x+x^2}}{3^x-1} \\ & \times \frac{\sqrt{1+x^2}+\sqrt{1-x+x^2}}{\sqrt{1+x^2}+\sqrt{1-x+x^2}} \\ & =\lim _{x \rightarrow 0}…
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