can anyone give an example of functions f and g such that

lim x-> inf of f/g = 1 but lim x->inf of e^f/e^g is not 1?

That's what 29 is saying, right? Thanks.

f = sin(x)

g = x

f/g tends to 1 (check with lhospitals rule)

Edit: Sorry I was thinking as x tended toward 0 Ignore everything .

e^f oscillates between [1/e,e]

x^sin(x) oscillates as well but with increasing amplitude end up going from [0,Infinity]

thus e^f / g^f does not even converge as x tends to infinity

g = x

f/g tends to 1 (check with lhospitals rule)

Edit: Sorry I was thinking as x tended toward 0 Ignore everything .

e^f oscillates between [1/e,e]

x^sin(x) oscillates as well but with increasing amplitude end up going from [0,Infinity]

thus e^f / g^f does not even converge as x tends to infinity

Last edited by moo5003 on Thu Oct 16, 2008 5:41 pm, edited 1 time in total.

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