Question

Am I starting right: Show lim...(1+x/n)^n = e^x

Answer 1

Question:
Show that the \[\lim_{n \rightarrow \infty}(1 + \frac{ x }{ n })^n = e^x (x>0)\]

Answer 2

x can actually be any number

Answer 3

lny = lim... ln(1+(x/n)^n
y'/y = n(lim... ln1 + (ln(x) - ln(n))
= n(lim... (1/x) + (1/x) - (n'/n))

Answer 4

lim... means \[\lim_{n \rightarrow \infty}\]

Answer 5

you might want to try that again

Answer 6

am I just suppose to find a definition for e
where the whole definition is to the x (or what)?

Answer 7

so there is no logarithmic differentiation?

Answer 8

there is...you did it wrong

Answer 9

OK, I'll try again later. Thanks

Answer 10

I assume you are trying to use L'Hospitals rule (you should be). Remember that only works with 0/0 or infinity /infinity