Let y = y ( x ) be a differentiable function in the interval ( 0 , ) such that y ( 1 ) = 2 , and lim t x ( t 2 y ( x ) - x 2 y ( t ) x - t ) = 3 for each x 0 . Then 2 y ( 2 ) is equal to [2026]

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Solution

Q.
Let $y = y (x)$ be a differentiable function in the interval $(0, \infty)$ such that $y (1) = 2$ , and $\lim_{t \to x} (\frac{t^{2} y (x) - x^{2} y (t)}{x - t}) = 3$ for each $x > 0$ . Then $2 y (2)$ is equal to [2026]

1 23

2 27

3 18

4 12

Ans.
(1)

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