CHAPTER 12 - Multivariable functions and partial derivatives

Section 12.1, page 914

Problem 25

First we'll do a 3D plot:

>	plot3d(4*x^2+y^2,x=-3..3,y=-5..5,axes=boxed);

You get the idea, but if we display it with contours, it's better:

>	plot3d(4*x^2+y^2,x=-3..3,y=-5..5,style=patchcontour,axes=boxed);

So you can guess what the contour plot will look like:

>	with(plots,contourplot):

>	contourplot(4*x^2+y^2,x=-3..3,y=-4..4,scaling=constrained,contours=[1,2,3,4,5,6,7,8],grid=[80,80],color=blue,thickness=2);

Section 12.2, page 921

Problem 12

Maple doesn't do two-variable limits. We can do iterated limits, which give evidence for, but not proof of existence of a limit.

>	limit(limit((cos(y)+1)/(y-sin(x)),x=Pi/2),y=0);

>	limit(limit((cos(y)+1)/(y-sin(x)),y=0),x=Pi/2);

So the limit is (probably) -2.

Section 12.3, page 931

Problem 30

>	f:=y*z*ln(x*y);

>	Diff(f,x)=diff(f,x);

>	Diff(f,y)=diff(f,y);

>	Diff(f,z)=diff(f,z);