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Calc I by Robert Miller

By Robert Miller

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Well, that's it. With a little practice you'll be like a pro! We'll do more examples, of course. You should practice the ones in this book. Before we do other examples, let us look at the right end of the curve that we drew above. In the top figure, can we find out how high M is? Yes! Later in this section we will. In the middle, could this be the right end? Perhaps, but we don't have enough info to know what the end looks like yet. In some very complicated cases, we might not ever be able to determine what the end is like (exactly).

Note 1 If the degree of the top is more than the bottom but not 1, there are no oblique asymptotes. Note 2 At most there is one oblique asymptote or one horizontal asymptote, but not both. There might be neither. Curve Sketching By the Pieces Before we take a long example, we will examine each piece. When you understand each piece, the whole will be easy. Example 11— The intercept is (4,0). We would like to know what the curve looks like near (4,0). Except at the point (4,0), we do not care what the exact value is for y, which is necessary in an exact graph.

In the second equation you will take the derivative and set it equal to 0. Let's start with an easy one. Example 1— A farmer wishes to make a small rectangular garden with one side against the barn. If he has 200 feet of fence, find the garden of maximum area. First we make what I call my crummy little picture. You only have to make the picture good enough so you can understand what you drew. Second, we assign variables. In this case, this task is easy. The two equations involve the area and the perimeter.

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