Each problem is worth 5 points.

1. What good is Mathematica? I mean, shouldn't I be able to do this stuff myself without a machine?

Among other things, Mathematica can draw pictures far better than most of us, and eventually we'll see plenty of instances where we need a good picture to know how to go about solving a problem ourselves. For now, try reproducing the sorts of things that have been appearing in the textbook. Generate a graph of the function f(x,y) = x² + y² together with the plane tangent to it at the point (1,2,5)
 

2. Fine, pretty pictures. But isn't it good for anything other than that?

How about times when we could do something, but we'd rather not spend all our time on the grunt work -- not to mention our chances of human error along the way. Mathematica makes a lot of things quick and easy. In class we struggled through some of the partial derivatives of the function f(x,y) = cos. Use Mathematica to find all first and second-order partial derivatives of this function. Are the mixed partials equal?
 

3. Okay, so it can save time too. But those were still things we could have managed ourselves if we'd wanted to badly enough. Does it do things we can't?

Sometimes it gives us insight to try things we otherwise wouldn't have thought of. Use Mathematica to investigate the shape of f(x,y) = . It turns out that approaching the origin along any straight line (like x=0, y=0, or y=x, the sorts of things we did in §12.2) gives a limit of 0, but the function still isn't continuous there. Figure out what curve of approach to use to show that  does not exist.
 

4. Okay, but you have to admit that I needed to know a lot of calculus to do that. Aren't you just saying that a person who knows enough math can use this?

Certainly you have to know something to make this work for you, but there are times when Mathematica will let you accomplish tasks you haven't yet learned the formal proceedures for. Consider this: The paraboloid z = x² + y² is sliced by the plane z = 2x + 2y. What shape is the curve of intersection, and what's the highest point on that curve?
 

5. Okay, fine, it's great -- but don't tell me it doesn't have any drawbacks at all!

Oh, it has lots of drawbacks, even apart from the sheer frustration of using it. Maybe the best way to get a feeling for this is to see how it can fit together with work done by hand to solve very difficult problems. Try problem 97 in §12.3 of Stewart, using Mathematica where you can.