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Limits Continuity and Differentiability question

2020 · 4 Sep · Shift 2 · Q29

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JEE Main
Mathematics
Limits Continuity and Differentiability
2020 · 4 Sep · Shift 2 · Q29

Limits Continuity and Differentiability question

2020 · 4 Sep · Shift 2 · Q29

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

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 :

A
${1 \over e}$
B
e
C
${1 \over 2e}$
D
2e

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