Question

(1 - 5/x)^x with lim ->infinity

Answer 1

is it e^5?

Answer 2

as x gets large; 5/x goes to zero; which leaves 1^inf .... is say it goes to 1

Answer 3

well, wolfram says it e^(-5)

Answer 4

http://www.wolframalpha.com/input/?i=lim {x+to+infinity}%281+-+5%2Fx%29^x

Answer 5

thank you!

Answer 6

\(\infty^0\) is one of the standard indeterminate forms. For this you must employ l'Hopital's rule.

http://en.wikipedia.org/wiki/Indeterminate_form#List_of_indeterminate_forms

Answer 7

\[\lim_{x\to \infty}\left(1+\frac{r}{x}\right)^{xt}=e^{rt}\]

replace r by -5 and t by 1

Answer 8

Yeah, if you know all the different forms of e you can just do it by sight ;)