Let f(x)=√lim_(r→ x)[2r²((f(r))²-f(x)f(r))/(r²-x²)-r³e^(f(r)/r)]… | JEE Main 2024 Mathematics PYQ

NVAHardJEE Main 2024 · 29 January, Shift 2Linear Differential Equations

Let $f(x)=\sqrt{\lim_{r\to x}\left[\frac{2r^2\left((f(r))^2-f(x)f(r)\right)}{r^2-x^2}-r^3e^{f(r)/r}\right]}$ 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:

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