I'm practicing for an exam coming up and i realized that i have a very small grasp on how to do these types of questions. if you can help, it would be greatly appreciated.

lim
x->infinity

(x/(x+1))^x

lim
x->1

x^(3/(x^3-1))

lim
x->0

(sin^2(3x)+1)^(cot(8x^2))

thanks for all help in advance.