- #1
mathmathRW
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I have been asked to prove the following limit relations.
(a) lim(as x goes to infinity) (b^x-1)/x = log(b)
(b) lim log(1+x)/x = 1
(c) lim (1+x)^(1/x) = e
(d) lim (1+x/n)^n =e^x
Unfortunately, I really have no idea where to start. We have a theorem that says if f(x)=the sum of (c sub n)*(x^n) then the limit of f(x) is the sum of c sub n. Is that useful for this problem? Any suggestions on how to do this?
(a) lim(as x goes to infinity) (b^x-1)/x = log(b)
(b) lim log(1+x)/x = 1
(c) lim (1+x)^(1/x) = e
(d) lim (1+x/n)^n =e^x
Unfortunately, I really have no idea where to start. We have a theorem that says if f(x)=the sum of (c sub n)*(x^n) then the limit of f(x) is the sum of c sub n. Is that useful for this problem? Any suggestions on how to do this?