Let f(x) be a continuously differentiable function on the interval (0, \infty) such that f(1)=2 and \lim_{t \rightarrow x} {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 [JEE Adv 2024 P1]

Correct Answer is : 911x+1311x10

\frac{31}{11 x}-\frac{9}{11} x^{10}

\frac{9}{11 x}+\frac{13}{11} x^{10}

\frac{-9}{11 x}+\frac{31}{11} x^{10}

\frac{13}{11 x}+\frac{9}{11} x^{10}

Differential Equations

Section: Mathematics

Question : 3 of 23

Marks: +1, -0

Let f(x) be a continuously differentiable function on the interval (0,∞) such that f(1)=2 and

lim

t⟶x

‌

t10f(x)−x10f(t)

t9−x9

=1
for each x>0. Then, for all x>0,f(x) is equal to

[JEE Adv 2024 P1]

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