WBJEE · Maths · Limits
The limit of \(\left\{\frac{1}{x} \sqrt{1+x}-\sqrt{1+\frac{1}{x^{2}}}\right\}\) as \(x \rightarrow 0\)
- A does not exist
- B is equal to \(\frac{1}{2}\)
- C is equal to 0
- D is equal to 1
Answer & Solution
Correct Answer
(B) is equal to \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\(\lim _{x \rightarrow 0}\left\{\frac{\sqrt{1+x}}{x}-\sqrt{1+\frac{1}{x^{2}}}\right\}\) \(=\lim _{x \rightarrow 0}\left\{\frac{\sqrt{1+x}-\sqrt{1+x^{2}}}{x}\right\}\left(\frac{0}{0}\right.\) form \()\)…
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