I have a problem xe^(1/x) and i'm supposed to use l'hospital's rule to explain its behavior as x -> 0. But L'hospital's rule is for division only I thought? Any help would be great thanks.
we spoke about a problem similar to this just tonight. I'll find the post for you. but the short answer is:
note that we can write x as 1/(1/x)
so xe^(1/x) = 1/(1/x) * e^(1/x) = [e^(1/x)]/(1/x) ........this is a quotient, however, this goes to 1/infinity, which is not a condition to use l'hopital's, i think you left out an x somewhere or something
see http://www.mathhelpforum.com/math-he...e-inf-inf.html
lim{x-->oo}xe^(1/x)
= lim{x-->oo}(1/(1/x))e^(1/x)
= lim{x-->oo} [e^(1/x)]/(1/x) .......this goes to inf/inf as x-->0, we can use l'hopital's
Apply L'hopital's
=> lim{x-->oo}[e^(1/x)]/(1/x) = lim{x-->oo}[(-x^-2)e^(1/x)]/(-x^-2)
= lim{x-->oo} e^(1/x)
= infinity
UMStudent here is a good website I discovered earlier today. It goes through all of the possible scenarios. Just keep working with it and you will pick it up rather quickly.
http://spot.pcc.edu/~sperry/M252_S-4_5.pdf