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Is -inf/0 an indetermination?
How much is lim (x->0, x>0) (ln x /x)
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- Randy PLv 71 decade agoFavorite Answer
(ln x)/x = (ln x) * (1/x)
The first term goes to -inf as x->0+, the second term goes to +infinity as x->0+. So the product goes to -infinity.
For a more formal proof, use an epsilon-delta style argument. Consider any large negative value -M. Show that for all x small enough, for all x in (0, delta), then (ln x)/x < -M
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