Let f be a differentiable function in the interval (0, ∞) such that f(1)=1 and lim t → x (t² f(x)-x² f(t))/(t-x)=1 for each x>0. Then 2 f(2)+3 f(3) is equal to _ _ _ _ _.

Limit, Continuity and Differentiability: JEE Main 2024 Mathematics question

JEE Main 2024 · 5 Apr, Morning shift · Q40

JEE Main 20245 Apr, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

Let

f

be a differentiable function in the interval

(0, \infty)

such that

f(1)=1

and

\lim _\limits{t \rightarrow x} \frac{t^2 f(x)-x^2 f(t)}{t-x}=1

for each

x>0

. Then

2 f(2)+3 f(3)

is equal to _________.

Your answerType your answer. Integers and decimals are accepted.