limt test

Q1) Show, by applying the limit test, that each of the following is true. a) The functions f(n)= n(n-1)/2 and g(n)= n^2 grow asymptotically at equal rate b) The functions f(n)=log n grow asymptotically at slower rate than g(n)=n. Q2) Show that log (n!) = Θ (nlog n);