WBJEE · Maths · Limits
\(\lim _{x \rightarrow 1}\left(\frac{1+x}{2+x}\right)^{\frac{(1-\sqrt{x})}{(1-x)}}\) is equal to
- A 1
- B does not exist
- C \(\sqrt{\frac{2}{3}}\)
- D ln 2
Answer & Solution
Correct Answer
(C) \(\sqrt{\frac{2}{3}}\)
Step-by-step Solution
Detailed explanation
We have, \(\lim _{x \rightarrow 1}\left(\frac{1+x}{2+x}\right)^{\frac{1-\sqrt{x}}{1-x}}\) \(=\lim _{x \rightarrow 1}\left(\frac{1+x}{2+x}\right)^{\frac{1-\sqrt{x}}{(1+\sqrt x)(1- \sqrt x)}}\) \(=\lim _{x \rightarrow 1}\left(\frac{1+x}{2+x}\right)^{\frac{1}{1+\sqrt{x}}}\)…
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