m223Review

# m223Review - 1 MATH 223 REVIEW PROBLEMS 1 You are in a...

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1 MATH 223 REVIEW PROBLEMS 1. You are in a nicely heated cabin in the winter. Deciding that it’s too warm, you open a small window. Let be the temperature in the room, minutes after the window was opened, feet from the window. (a) Is an increasing or decreasing function of ? Explain. (b) Is an increasing or decreasing function of ? Explain. 2. Consider the following sets of points in space: A is the set of points whose distance from the -axis is . B is the set of points whose distance from the -plane is . C is the set of points whose distance from the -axis is equal to its distance to the -plane. Describe in words, write equations, and give a sketch for each of these sets of points. 3. Describe in words the intersection of the surfaces and , sketch it, and give simpliFed equations for it. 4. Each of the graphs in ±igure 1 shows the quantity that can be sold of a certain product (Product ), as a function of its price and the price of another product (Product ). (a) (b) (c) Figure 1 Choose which graph Fts best and explain why if: (a) Product is ²ashlights and Product is batteries. (b) Product is domestic cars and Product is imported cars. 5. Match each of the following functions in (a)-(f), given by a formula, to the corresponding table of numerical values, graph and/or contour maps (i)-(xi). Some formulas may match NONE or MORE THAN ONE of the representations (i)-(ix). (a) (b) (c) (d) (e) (f)

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2 (i) Table 1 (ii) Table 2 (iii) Table 3 (iv) Figure 2 (v) Figure 3 (vi) Figure 4 (vii) Figure 5 (viii) Figure 6 (ix) Figure 7

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m223Review - 1 MATH 223 REVIEW PROBLEMS 1 You are in a...

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