No one? I thought these were simple If anyone has any suggestions, please tell me.
I'm having some difficulty with these two limits. I learned this stuff a while back, but as you know, you sometimes forget the simple stuff after you havent done it in a while.
1:
limit as x goes to infinity of [(x+1)(x+1)^x]/(x^x)
*note, only the second x+1 is raised to the power of x in the numerator
2:
limit as x goes to infinity of [x/(x+1)]^x
Thanks!
Look at what happens to the log of f(x)=[(x+1)(x+1)^x]/(x^x).
log(f(x)) = log(x+1) + x log(x+1) -x log(x)
............= log(x+1) + x log(1+1/x))
The first term goes to infty as x goes to infty, and whatever the second term
does it is positive for positive x and so log(f(x)) goes to infty as x goes to
infty and hence so does f(x).
RonL