Let f(x) be differentiable on the interval (0, ∞) such that f(1) = 1, and lim_t → x (t^2 f(x) - x^2 f(t))/(t - x) = 1 for each x > 0. Then, f(x) is

Let f(x) be differentiable on the interval (0, ∞) such that… — JEE Main 2007 Mathematics PYQ

AIEEE 2007

Let

f(x)

be differentiable on the interval

(0, \infty)

such that

f(1) = 1

, and

\lim_{t \to x} \frac{t^2 f(x) - x^2 f(t)}{t - x} = 1

for each

x > 0

. Then,

f(x)

Show answer

Correct option: A

[AIEEE 2007]

Practise Limits Continuity and Differentiability the way it is asked

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