Let f:(0,∞) → (0,∞) be a differentiable function such that f(1) = e and lim t → x (t²f²(x) - x²f²(t))/(t - x) = 0. If f(x) = 1, then x is equal to:

Limit, Continuity and Differentiability: JEE Main 2020 Mathematics question

JEE Main 2020 · 4 Sep, Evening shift · Q4194

JEE Main 20204 Sep, Evening shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

Let

f:\left( {0,\infty } \right) \to \left( {0,\infty } \right)

be a differentiable function such that f(1) = e and

\mathop {\lim }\limits_{t \to x} {{{t^2}{f^2}(x) - {x^2}{f^2}(t)} \over {t - x}} = 0

. If f(x) = 1, then x is equal to :

JEE Main 2020 · 4 Sep, Evening shift · Q4194

JEE Main 20204 Sep, Evening shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

Let

f:\left( {0,\infty } \right) \to \left( {0,\infty } \right)

be a differentiable function such that f(1) = e and

\mathop {\lim }\limits_{t \to x} {{{t^2}{f^2}(x) - {x^2}{f^2}(t)} \over {t - x}} = 0

. If f(x) = 1, then x is equal to :