Duration: 5:46

2 views

0

Let \( f:(0, \infty) \rightarrow \mathrm{R} \) be a differentiable function such that
\( f^{\prime}(x)=2-\frac{f(x)}{x} \) for all \( x \in(0, \infty) \) and \( f(1) \neq 1 \)
P
Then
[JEE Advanced-2016]
(a) \( \lim _{x \rightarrow 0+} f^{\prime}\left(\frac{1}{x}\right)=1 \)
(b) \( \lim _{x \rightarrow 0+} x f\left(\frac{1}{x}\right)=2 \)
(c) \( \lim _{x \rightarrow 0+} x^{2} f^{\prime}(x)=0 \)
(d) \( |f(x)| \leq 2 \) for all \( x \in(0,2) \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live