`lim_(x->0^+) ln(x)/x` Find the limit. Use l’Hospital’s Rule where appropriate. If there is a more elementary method, consider using it. If l’Hospital’s Rule doesn’t apply,...

`lim_(x->0^+) ln(x)/x` Find the limit. Use l’Hospital’s Rule where appropriate. If there is a more elementary method, consider using it. If l’Hospital’s Rule doesn’t apply, explain why.

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Textbook Question

Chapter 4, 4.4 - Problem 19 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to evaluate the given limit, such that:

`lim_(x->0^+) (ln x)/x = (ln 0^+)/(0^+)`

`lim_(x->0^+) (ln x)/x = (-oo)*1/(0^+)`

`lim_(x->0^+) (ln x)/x = -oo*(+oo) = -oo`

Hence, evaluating the given limit yields using the rule that the limit of the product is the product of the limits, yields `lim_(x->0^+) (ln x)/x = -oo.`

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