Assignment For Section 1.2 & 1.3

Remember that you are responsible for all definitions and examples. But you need not memorize conversions, just know where to look them up in the text. Also remember to keep the answers to the reading questions on a separate piece of paper; these will be randomly collected from time to time.

1)   Example 3a on page 16 discusses a method for finding the maximum height of a ball thrown straight upwards from the ground. Your also discuss how to find maximums in your Calc 1 class. How does the method discussed in this example compare to the methods you used in Calc 1?

2)   Figures 1.2.1 and 1.2.2 on page 11 illustrate that adding a constant to a graph produces a parallel graph. We know from calculus that if a function has an antiderivative then there are several antiderivatives of the given function. Furthermore any two antiderivatives of the given function differ by some constant. Use your Calculus knowledge to graphically explain why the following statement is true:

If F(x) is an antiderivative of f(x), then G(x)=F(x) + c is also an antiderivative of f(x). Note that c represents some arbitrary constant. Also note that you could explain the above by stating that since the derivative of a constant is zero both F and G have the same derivative. This would not be a graphical explanation, so this is not what I am asking for. 3)   Define solution curve, directional field, and isocline. Be sure to include examples to clarify your definitions.

4)   Determine the hypothesis and the conclusion of theorem 1 on page 23. Be sure to define any unclear mathematical terms

Note that the remarks following the theorem show that the conclusion could be true or false when the hypothesis is not fulfilled. The remarks also show that the arbitrary open interval, J, of the conclusion might not be the entire interval you started with. This is how you should tear apart a theorem when reading science or technology texts or journals. Problems:

page 17     2, 5, 8, 9, 13, 17, 20, 21, 27, 31 ( ?), 32

page 25     [2, 3, 7, 10]*, 11, 14, 15, 21, 23, 24, 25, 28, 31, 34

*See xeroxed sheet. Draw a few for each problem, and then check the back of your text.