please I need a step by step solution for the question above

Problem 1.10. (a) For a given workload, the number of jobs completed by a server at time t is given by w(t)=3t2/(9t+1). (i) Compute the throughput of this server as a function of time and find its limit as t. (ii) Compute its average throughput, X. (iii) Compute the marginal service time of jobs running on this system and use it to find the average service time Ts. (iv) Verify that XTs=1. (b) The number of jobs carried out by a server at time t is given by x(t)= 100ln(t+1)/(t+1). Compute the marginal and average service times of jobs as t, and verify that the product of marginal service time with marginal throughput and the product of average service time with throughput are both equal to 1. (c) The marginal service time of jobs on a server is given by s(w)=1+ (w2+1)/(100w). Compute the throughput of this server as a function of time and determine the number of jobs completed in 100 seconds