Question:On a couple of the problems in practice exams I was able to solve the problems without using
some of the more advanced multivariable calculus methods we've learned
Can we assume that any correct method of solving the problem will be
given full credit on an exam?

Answer:
If you get through with an other method and everything is 100% correct,
we give full credit. This is sometimes possible, like in Lagrange
problems. But there are often pitfalls. You might get the right result
with single variable methods, but these solutions are
in general wrong or incomplete because boundary conditions
are forgotten. Then graders often do not give any credit, not even partial credit.
In general, we do not advise to be "sneaky" in exams (not only in mathematics).
It is not appreciated and alternative solutions (even if clever) are often
not recognized by graders because of the time constraints they have with grading.
If you have time in the exam, you can do both methods to
check your answer. We try to avoid solutions, where alternative
methods are successful. Most of the time, alternative solution methods
just are much more complicated or lead to a trap and most graders do not give
any partial credit for solution attempts with a shortcut which does not work.

Question:I love the pictures Mathematica can make, and want to make myself a
desktop wallpaper from them. Do you know if there's a way of setting
the size of the output image?

Answer:
S=Plot3D[Sin[x y],{x,0,5},{y,0,5},Background>RGBColor[0,0,0],Boxed>False,Axes>False]
Export["image.jpg",S,"JPG",ImageSize>{1600,1200}]
would produce a nice background picture for a 1600x1200 pixel monitor.
