Let f(x) be a continuously differentiable function on the interval (0,∞) such that f(1)=2 and displaystylelim_t→ xfract^10f(x)-x^10f(t)t^9-x^9=1 for each x>0. Then, for all x>0, f(x) is equal to

Let f(x) be a continuously differentiable function on the… — JEE Advanced 2024 Mathematics PYQ

JEE Advanced 2024 · Paper 1

Let

f(x)

be a continuously differentiable function on the interval

(0,\infty)

such that

f(1)=2

and

\displaystyle\lim_{t\to x}\frac{t^{10}f(x)-x^{10}f(t)}{t^{9}-x^{9}}=1

for each

x>0

. Then, for all

x>0

f(x)

is equal to

Show answer

Correct option: B

[JEE Advanced 2024 · Paper 1]

Practise Limits Continuity and Differentiability the way it is asked

A timed set of real JEE Advanced Limits Continuity and Differentiability questions, graded as the exam grades. No sign-up.