Maple Commands for Chapter 14 (Stewart)1. Graph the functionGraph z = f(x, y). In this example, z =p9 − x2− y2f:=(x,y)->sqrt(9-x^2-y^2);plot3d(f(x,y),x=-3..3,y=-3..3);Note that when you click your mouse on the graph, you can spin it around. You canalso change how the axes look, put on a legend, change the coloring, etc. Experimentwith the menu options (with the black box around the figure- otherwise, you getthe regular menu options).2. Plot the level curvesPlot the level curves (also called contours) of the function z = f(x, y). TheMaple command is contourplotwith(plots):contourplot(sin(x*y),x=-3..3,y=-3..3);3. Multiple Limits.EXAMPLE: Does lim(x,y ) →(0 ,0)x2− y2x2+ y2exist?limit( (x^2-y^2)/(x^2+y^2), {x=0, y=0} );EXAMPLE: Use a graph of the function to determine if the following limit exists:lim(x,y ) →(0, 0)2x2+ 3xy + 4y23x2+ 5y2f:=(x,y)->(2*x^2+3*x*y+4*y^2)/(3*x^2+5*y^2);plot3d(f(x,y),x=-1..1,y=-1..1);4. Partial Derivatives:Example: If f(x, y, z) = xexyln(z), compute all first partial derivatives and allsecond partials involving x and z.f:=(x,y,z)->x*exp(x*y)*ln(z);fx:=diff(f(x,y,z),x); #This is the partial of f w/r to xfy:=diff(f(x,y,z),y);fz:=diff(f(x,y,z),z);fxx:=diff(fx,x);fxz:=diff(fx,z);fzx:=diff(fz,x);fzz:=diff(fz,z);5. Tangent PlanesFind the expression for the tangent plane, and plot the plane together with thefunction.EXAMPLE: If f(x, y) = xexy, plot z = f (x, y) together with the tangent planeto f at x = 1, y = 1.12First, rewrite the equation of the tangent plane:z = z0+ fx(x0, y0)(x − x0) + fy(x0, y0)(y − y0)Using Maple:f:=(x,y)->x*exp(x*y);fx:=diff(f(x,y),x);fy:=diff(f(x,y),y);fx1:=subs({x=1,y=1},fx);fy1:=subs({x=1,y=1},fy);P:=f(1,1)+fx1*(x-1)+fy1*(y-1);plot3d({f(x,y),P},x=-1..3,y=-1..3,view=0..5,axes=’boxed’);6. The Chain Rule(See Example 5, p. 921 of Stewart’s Calc)If u = x4y + y2z3, and x = rset, y = rs2e−t, and z = r2s sin(t), find the value of∂u∂swhen r = 2, s = 1, t = 0.In Maple:x:=r*s*exp(t);y:=r*s^2*exp(-t);z:=r^2*s*sin(t);u:=x^4*y+y^2*z^3;h:=diff(u,s);h1:=subs({r=2,s=1,t=0},h);evalf(h1);7. Implicit Differentiation:If F (x, y) = 0, thendydx=−FxFyEXAMPLE: Find y0if x3+ y3= 6xy.In Maple:F:=x^3+y^3-6*x*y;dydx:=diff(F,x)/diff(F,y);8. The GradientCompute the Gradient, ∇f = [fx, fy, fz]In Maple, if f(x, y, z) = 3x2+ 2yz, then the gradient is:with(linalg):grad(3*x^2+2*y*z, vector([x,y,z]));9. Contours and GradientsPlot the contours of f (x, y) = x2− y2, together with some gradient vectors (SeeFigure 13, pg.