Big O notation

i) Show that x^3 is O(x^4) but x^4 is not O(x^3)
ii)Show that xlnx is O(x^2) but x^2 is not O(xlnx)
iii)Show that  a^x O(b^x)  but b^x is not O(a^x)
if 0 < a <  b  (0 = zero)

iv)Show that 1^k + 2^k+...+n^k is O(n^(k+1)) for every positive integer k