Let f:(0,\infty)\toR be a differentiable function such that f'(x)=2-{f(x)}/x for all x ∊(0,\infty) and f(1)\neq1.Then [JEE Adv 2016 P1]

Correct Answer is : limx→0+f′(1x)=1

\text{lim}_{x\to0^{+}}f'(1/x)=1

\text{lim}_{x\to0^{+}}xf(1/x)=2

\text{lim}_{x\to0^{+}}x^2f'(x)=0

|f(x)|\leq2 for all x ∊ (0,2)

Differential Equations

Section: Mathematics

Question : 13 of 23

Marks: +1, -0

Let f:(0,∞)→R be a differentiable function such that f′(x)=2−

f(x)

for all x∊(0,∞) and f(1)≠1.Then

[JEE Adv 2016 P1]

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