AP EAMCET · Maths · Limits
Let \(f(x)=\sqrt{\frac{x}{1-x}}+\sqrt{\frac{1-x}{x}}\). If \(\lim _{x \rightarrow m} f(x)=5 / 2\), then set of all possible finite values of 1 and \(m\) is
- A \(\{0,1\}\)
- B \(\left\{0, \frac{1}{3}, \frac{2}{3}\right\}\)
- C \(\left\{0, \frac{2}{5}, \frac{3}{5}\right\}\)
- D \(\left\{\frac{1}{5}, \frac{4}{5}\right\}\)
Answer & Solution
Correct Answer
(D) \(\left\{\frac{1}{5}, \frac{4}{5}\right\}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { } \lim _{x \rightarrow m} f(x)=\lim _{x \rightarrow m} \sqrt{\frac{x}{1-x}}+\sqrt{\frac{1-x}{x}} \\ & 5 / 2=\lim _{x \rightarrow m} \frac{x+(1-x)}{\sqrt{x(1-x)}}=\lim _{x \rightarrow m} \frac{1}{\sqrt{x-x^2}} \\ & \Rightarrow \quad…
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