Limit EvaluationDate: 7/7/96 at 16:21:41 From: Anonymous Subject: Limit Evaluation I'm in the first year of electronics in Buenos Aires and I have a problem with a limit. I have no idea how to begin: Lim Root x of (x) X -> oo Limit of root X of x, with X -> infinity. Date: 7/7/96 at 19:3:28 From: Doctor Anthony Subject: Re: Limit Evaluation I believe you are wanting the xth root of x, which is better shown as x^(1/x) Let y = x^(1/x) Now, with a variable as a power, it is usual to take logs. Take logs (base e) of both sides ln(y) = (1/x)ln(x) = ln(x)/x Now as x -> infinity this becomes inf/inf and we can use l'Hopital's rule to see what the ratio is becoming as x approaches its limit. LT(as x->infin.)ln(y) = (diff. of top line)/(diff. of bottom line) = (1/x)/1 = 1/x ->0 as x -> infin. If ln(y) -> 0 then y -> 1 and so Lt(as x-> infin.) x^(1/x) = 1 -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/ Date: 7/7/96 at 20:58:21 From: Anonymous Subject: Re: Limit Evaluation Thank you Mr. Anthony, this is the best WWW of math!! Hernan Gabriel Zapata. (archie@giga.com.ar) |
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