This is an example of a last-minute reminder. It should be removed from the worksheet after you have done what it suggests: Like any worksheet that you submit, this oneshould have a header containing your name, your section number, the lab number, and any other information requested by the instructor.0. Setup.restart;with(plots): with(DEtools):1. Expressions, derivatives and graphs.The practice expression.f0:=exp(sin(x));f1:=diff(f0,x);f2:=diff(f1,x);fvars:=x=-2*Pi..2*Pi,y=-3..3;pf0:=plot(f0,fvars,color=RED):pf1:=plot(f1,fvars,color=GREEN):pf2:=plot(f2,fvars,color=BLUE):display({pf0,pf1,pf2},title="Practice graphs");A new expression.Definitions.Plots.Limits.limit(g0,x=0);limit(g1,x=0);limit(g2,x=0);Refined plots.Discussion.Only positive values of x appear.Behavior of graphs near x=0.2. Implicit functions.A contour plot.ex2:=1.3*ln(F)-0.8*F+ln(R)-1.1*R;FRwindow := R=0.1..4,F=0.1..6;contourplot(ex2,FRwindow,title="R versus F");Discussion.3. Simple Mechanics.The equation and initial condition.de3:=diff(y(t),t,t)=-g; ic3:=y(0)=h,D(y)(0)=v; Solving the equation and checking the result.ans3:=dsolve({de3,ic3});eval(de3,ans3);Initial condition on position.Initial condition on velocity.Discussion.4. From the textbook.Section 1.1, Exercise 31.eq31:=diff(y(t),t)=2*t-1-y(t)^2;ic31:={[y(0)=0],[y(1)=0],[y(3)=0]};Solution (Graph).DEplot(eq31,y,t=-1..5,ic31,y=-3..3,title="Exercise 31");Explicit solution.infolevel[dsolve]:=3;dsolve(eq31);Discussion.