demo.sagews

n = var('n')
assume(x>1)
f(x) = x ^ n
f.limit(n=infinity)

x |--> +Infinity

n = var('n')
forget()  # Need to forget previous assumption
assume(0 < x)
assume(x < 1)
f(x) = x ^ n
f.limit(n=infinity)

x |--> 0