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Differential Equations question

2016 · Shift 1 · Q32

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JEE Advanced
Mathematics
Differential Equations
2016 · Shift 1 · Q32

Differential Equations question

2016 · Shift 1 · Q32

JEE AdvancedMathematicsDifferential EquationsMultiple correct+4 / −2

Let

f:(0,\infty ) \to R

be a differentiable function such that

f'(x) = 2 - {{f(x)} \over x}

for all

x \in (0,\infty )

and

f(1) e 1

. Then

A
$\mathop {\lim }\limits_{x \to {0^ + }} f'\left( {{1 \over x}} \right) = 1$
B
$\mathop {\lim }\limits_{x \to {0^ + }} xf\left( {{1 \over x}} \right) = 2$
C
$\mathop {\lim }\limits_{x \to {0^ + }} {x^2}f'(x) = 0$
D
$\left| {f(x)} \right| \le 2$ for all $x \in (0,2)$

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