JEE Mains · Maths · STD 12 - 9. differential equations
Let \(f(x)=\sqrt{\lim _{r \rightarrow x}\left\{\frac{2 r^2\left[(f(r))^2-f(x) f(r)\right]}{r^2-x^2}-r^3 e^{\frac{f(r)}{r}}\right\}}\) be differentiable in \((-\infty, 0) \cup(0, \infty)\) and \(f(1)=1\). Then the value of \(ea\), such that \(f(a)=0\), is equal to ...........
- A \(5\)
- B \(7\)
- C \(2\)
- D \(4\)
Answer & Solution
Correct Answer
(C) \(2\)
Step-by-step Solution
Detailed explanation
\( f(1)=1, f(a)=0 \) \( f^2(x)=\operatorname{Lim}_{r \rightarrow x}\left(\frac{2 r^2\left(f^2(r)-f(x) f(r)\right)}{r^2-x^2}-r^3 e^{\frac{f(r)}{r}}\right) \)…
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