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

Limits, differentiation, related rates, integration, trig integrals, etc.

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

Postby rogermiranda on Mon Sep 26, 2011 5:53 pm

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

Postby maggiemagnet on Mon Sep 26, 2011 10:15 pm

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

Postby rogermiranda on Tue Sep 27, 2011 2:41 pm

It is the limit of (1/x) + ln(x). Thanks! Please help. I really appreciated!! :D
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Re: Calculus 2 (limits): limit as x -> 0+ of 1/x + lnx  TOPIC_SOLVED

Postby maggiemagnet on Tue Sep 27, 2011 7:18 pm

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

Postby rogermiranda on Wed Sep 28, 2011 2:55 pm

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

Postby maggiemagnet on Wed Sep 28, 2011 6:27 pm

rogermiranda wrote: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.
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