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**Sample text**

1 Limits, Rates of Change, and Tangent Lines 35 25. The graphs in Figure 13 represent the positions s of moving particles as functions of time t. Match each graph with The fraction of a city’s population infected by a flu virus is plotted as a function of time (in weeks) in Figure 12. a description: (a) Which quantities are represented by the slopes of lines A and B? Estimate these slopes. (a) Speeding up (b) Is the flu spreading more rapidly at t = 1, 2, or 3? (b) Speeding up and then slowing down (c) Is the flu spreading more rapidly at t = 4, 5, or 6?

X→9 3. lim lim x 4 14 1 x→x→−3 2 solution lim x 4 = x→ 12 1 4 1 . = 2 16 5. lim t −1 2/3 t→2 lim z z→27 solution 7. 1 lim t −1 = 2−1 = . 6. 3 9. Basic Limit Laws 2x 3 + 4x) lim (3x 4 − lim (3x 3 + 2x 2 ) x→−1 x→ 13 solution Using the Sum Law, the Constant Multiple Law and the Powers Law: lim (3x 4 − 2x 3 + 4x) = lim 3x 4 − lim 2x 3 + lim 4x x→−1 x→−1 x→−1 x→−1 = 3 lim x 4 − 2 lim x 3 + 4 lim x x→−1 x→−1 x→−1 = 3(−1)4 − 2(−1)3 + 4(−1) = 3 + 2 − 4 = 1. 2 − 9) 11. lim (x + 1)(3x x→2lim (3x 2/3 − 16x −1 ) x→8 solution Using the Product Law, the Sum Law and the Constant Multiple Law: lim (x + 1) 3x 2 − 9 = x→2 lim 3x 2 − lim 9 lim x + lim 1 x→2 x→2 x→2 x→2 = (2 + 1) 3 lim x 2 − 9 x→2 = 3(3(2)2 − 9) = 9.

The graphs in Figure 13 represent the positions s of moving particles as functions of time t. Match each graph with The fraction of a city’s population infected by a flu virus is plotted as a function of time (in weeks) in Figure 12. a description: (a) Which quantities are represented by the slopes of lines A and B? Estimate these slopes. (a) Speeding up (b) Is the flu spreading more rapidly at t = 1, 2, or 3? (b) Speeding up and then slowing down (c) Is the flu spreading more rapidly at t = 4, 5, or 6?