Unformatted text preview: respectively zero, 1, and ∞ . We can in fact turn this into a L’Hˆopital’s Rule problem: x ln x = ln x 1 /x = ln x x1 . Now as x approaches zero, both the numerator and denominator approach inﬁnity (one∞ and one + ∞ , but only the size is important). Using L’Hˆopital’s Rule: lim x → + ln x x1 = lim x → + 1 /xx2 = lim x → + 1 x (x 2 ) = lim x → +x = 0 . One way to interpret this is that since lim x → + x ln x = 0, the x approaches zero much faster than the ln x approaches∞ ....
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 Spring '07
 JonathanRogawski
 Math, Calculus, Limits, lim, Elementary arithmetic, 1 sec, Multiplicative inverse, 83 sec

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