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> Suppose that $f $ is differentiable on $(0,\infty) $ and $f'(t) \rightarrow b $ as $t\rightarrow + \infty$ . Show that $f (t)/t\rightarrow b $.
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I want to use mean value theorem here, but I can't figure out where. When $ f (0) \ne 0$, I can't make $f'(c)=\frac {f (t)-f (a)}{t-a} $ become $f (t)/t $. So now I am just not really sure what to do.