=+1. Prove the following order relations:

a) 1 − cos2 x = O(x2) as x → 0

b) ln x = o(xα) as x → ∞ for any α > 0

c) x2 1+x3 + ln(1 + x2) = O(x2) as x → 0

d) x2 1+x3 + ln(1 + x2) = O(ln x) as x → ∞.