2. Compare the asymptotic order of growth of the following pairs of function. In eaclh case, show what is the function that growths faster or if they grow at the same rate (hint: use limits). a) f(n) = 1 1 2n + log(m), g(n) = 2n + (log 2n)2 b) f(n) = nlog(n) + n, g(n) = nlog,(n) c) f(n) = n1/2, g(n) = n1/3 d) f(n) = 2n+2 g(n) = 22n