JEE Advance - Mathematics Hindi (2016 - Paper 1 Offline - No. 14)
मान लें $$f:(0,\infty ) \to R$$ एक अवकलनीय फलन है ऐसा कि $$f'(x) = 2 - {{f(x)} \over x}$$ सभी $$x \in (0,\infty )$$ के लिए और $$f(1) \ne 1$$। तब
$$\mathop {\lim }\limits_{x \to {0^ + }} f'\left( {{1 \over x}} \right) = 1$$
$$\mathop {\lim }\limits_{x \to {0^ + }} xf\left( {{1 \over x}} \right) = 2$$
$$\mathop {\lim }\limits_{x \to {0^ + }} {x^2}f'(x) = 0$$
$$\left| {f(x)} \right| \le 2$$ सभी $$x \in (0,2)$$ के लिए
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