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Limits Continuity and Differentiability question

2024 · 29 Jan · Shift 2 · Q59

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JEE Main
Mathematics
Limits Continuity and Differentiability
2024 · 29 Jan · Shift 2 · Q59

Limits Continuity and Differentiability question

2024 · 29 Jan · Shift 2 · Q59

JEE MainMathematicsLimits Continuity and DifferentiabilityNumerical+4 / −1

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

\underline{\hspace{2cm}}

.

Numerical answer

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