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Let f:(0,oo)->R be a differentiable func...

Let `f:(0,oo)->R` be a differentiable function such that `f'(x)=2-f(x)/x` for all `x in (0,oo)` and `f(1)=1`, then

A

`underset(xrarr0^(+))limf'((1)/(x))=1`

B

`underset(xrarr0^(+))limxf((1)/(x))=2`

C

`underset(xrarr0^(+))limx^(2)f'(x)=0`

D

`|f(x)|le2" for all "x in (0,2)`

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AI Generated Solution

To solve the problem step by step, we start with the given differential equation and the initial condition. ### Step 1: Write the given differential equation The given differential equation is: \[ f'(x) = 2 - \frac{f(x)}{x} \] ### Step 2: Rearrange the equation We can rearrange this equation to isolate \( f'(x) \): ...
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