Question 1. (a) Evaluate .OO -dx. x2 + 1 x (b) For what values of a does paz2 dx converge?Question 2. Consider a simple model for a population N(t) of marine invertebrates at time t, measured in days, where the per capita birth rate is proportional to the temper- ature of the ocean at time t, T(t), and the per capita death rate is proportional to the salinity of the ocean, S(t): dN dt = (bT(t))N - (dS(t) ) N. On the west coast of BC, a simple model for ocean temperature in degrees Celsius is T(t) = 9 - 3 cos (2xt and a simple model for ocean salinity in parts per thousand (ppt) is S(t) = 25 + 7 cos ( 2nt 365 , So the model becomes dN 2nt 2nt N. dt 6 9 - 3 cos N - d 25 + 7 cos 365 365 Find the population size N(t), with the initial condition N(0) = 100, (a) when b = 1/9 and d = 1/25, (b) when b = 4/9 and d = 1/25, and (c) when b = 1/9 and d = 4/25