Calculus 2 (limits): limit as x -> 0+ of 1/x + lnx

Limits, differentiation, related rates, integration, trig integrals, etc.
rogermiranda
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Calculus 2 (limits): limit as x -> 0+ of 1/x + lnx

Hello, I need help with this limit.

The limit as x approaches zero from the right of 1/x + lnx. The answer is positive infinity but I am not sure how to work the problem. I tried to combine the fraction and other algebra tricks but I get indeterimante forms. I tried L'Hopitals rule as well but could not get the right answer. Please help.

maggiemagnet
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Re: Calculus 2 (limits): limit as x -> 0+ of 1/x + lnx

The limit as x approaches zero from the right of 1/x + lnx. The answer is positive infinity...
Is the limit of (1/x) + ln(x) or of 1/(x + ln(x))?

rogermiranda
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Re: Calculus 2 (limits): limit as x -> 0+ of 1/x + lnx

maggiemagnet
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Re: Calculus 2 (limits): limit as x -> 0+ of 1/x + lnx

Have you done derivatives yet? If so, then find the critical point of y = (1/x) + ln(x). Then figure out what the function y = f(x) is doing on the two intervals. If the function is always decreasing on, say, the interval (0, 1), then what can you say about the value of the function as x gets close to zero from the right?

rogermiranda
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Re: Calculus 2 (limits): limit as x -> 0+ of 1/x + lnx

Thanks for the explanation. I have done lots of derivatives as I am now in second semester calculus. But I need to know how to evaluate this limit ALGEBRIACALLY and WITHOUT GRAPHING. Would you know how to work this problem using algebra? Thanks.

maggiemagnet
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Joined: Mon Dec 08, 2008 12:32 am
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Re: Calculus 2 (limits): limit as x -> 0+ of 1/x + lnx

Thanks for the explanation. I have done lots of derivatives as I am now in second semester calculus. But I need to know how to evaluate this limit ALGEBRIACALLY and WITHOUT GRAPHING. Would you know how to work this problem using algebra? Thanks.
Try following the steps I wrote out earlier. None of that involves drawing a graph.