1. (a). Write the MAT lab command for Three-dimensional piots typically display a surface defined by a function in two varibbles, z-f(x,y). For instance, calculate ayee x2y2 piven row and column voctors x and y with 20 points each in the range [2,2]. (b). Write the MAT lab command to Plot the sine, cosine fimetion over a lincarly spaced vector of values from 0 to 2i using a red dashed line in the same plot. 2. Given that the concentration of a specics A in a constant volume, batch reactor obeys this differential equation atC4=kCA with the initial candition O4(t=0)=2.3molL and k=0.25Emol/s. Plot the graph t vs C. 3.The following set of differential equations describes the change in concertration throe species in a tank. The reactions ABC oceur within the tank. The constants k, and k describe the reaction rate for AB and BC respectively. The following ODEs are obtained: dtdCa=k1CadtdCb=k1Cdk2CbdtdCc=k2Cb Where ki1h1 and k22hr1 and at time t-0, Cat-5mol and Cb-Cc=0mol. Solve the system of equations and plot the change in concentration of each species over time. 4. Penicitlin is produced is a batch reactor by fermentation. The reaction model is givin toy dtdt=1A1a21x2didx=a4 where A is the dimenionless cell concentration and Q is the dimensionlens penicilin carem(0)=0.028 and x(0)=0.0. Generate profiles of a and x2 as a function of dimenvionlese time: t(0i1). 5. A biological process involving the growth of a biomass from subtrate can be repetinented at. dtdB=K+SkBSdrdS=K+S0.75kBS when, B and S are the biounass and substrate concentrations, respectively. Solve there ditierential equatizks from t=0 to 20 . At t=0,S and R are S and 0.05 , respectively. The moction kinetics ane K=0.3 and K=0.000001