Find the limiting behavior of (1+(x/n))^nt as n goes to infinity.?

Answer 1

Edit2: e^(xt)

[I was missing the x :( ]

Answer 2

1

Answer 3

1 + (x/n)^nt
= 1 + [xn^(-1)]^nt
= 1 + x^[n^(+1)n^(-1)t]

the n's will cancel out
= 1 + x^t

so that the limit with no n's in the equation.

Answer 4

First we do the parenthesis and get 1.
1 to an infinite power is still 1.
ANSWER = 1.

Answer 5

e^h -one million for extremely small values of h is approximately = h So e^h is approximately = h +one million So e is approximately = (h+one million)^(one million/h) So lim (one million+h)^(one million/h) =e h-> 0 Or, set t=one million/h, then lim (one million+one million/t)^t =e t-> infinity For extra formal proofs see advantageous, Calculus, website seventy one or Smail, factors of the thought of countless strategies, pages 38-40-one.

Answer 6

e^t

lim ((1+(x/n))^n)^t = lim ((n+x)/n)^t = e^t
n->inf __________n->inf

x becomes negligible becuase lim (an+x)/bn= a/b
_______________________n->inf

Answer 7

e^(xt)