(20 points) Recall the following definitions: - A non-negative function f:NR is polynomially bounded, written f(n)=poly(n), if f(n)=O(nc) for some constant c0. 1 - A non-negative function :NR is negligible, written (n)=negl(n), if it decreases faster than the inverse of any polynomial. Formally: limn(n)nc=0 for any constant c0. (Otherwise, we say that (n) is non-negligible.) Are following functions necessarily negligible? Prove your answer. (Think: why doesn't the base of the logarithm matter in both cases?) (a) 1(n)=log(nlogn)1 (b) 2(n)=2(log2n)1 (c) 3(n)=f(n)v(n) where f(n)=poly(n),v(n)=negl(n) (d) 4(n)=v(n)1/logn where v(n)=negl(n) (e) 5(n)=e1n200v(n), where v(n) is a negligible function (f) 6(n)=v(n)1/50, where v(n) is a negligible function