121616949-math.8 - 234 10.2 Series 240 10.3 The Integral...

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viii Contents 9 Applications of Integration 177 9.1 Area between curves . . . . . . . . . . . . . . . . . . . . . . 177 9.2 Distance, Velocity, Acceleration . . . . . . . . . . . . . . . . . 182 9.3 Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 9.4 Average value of a function . . . . . . . . . . . . . . . . . . . 192 9.5 Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 9.6 Center of Mass . . . . . . . . . . . . . . . . . . . . . . . . . 200 9.7 Kinetic energy; improper integrals . . . . . . . . . . . . . . . 205 9.8 Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 9.9 Arc Length . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 9.10 Surface Area . . . . . . . . . . . . . . . . . . . . . . . . . . 222 9.11 Differential equations . . . . . . . . . . . . . . . . . . . . . . 227 10 Sequences and Series 233 10.1 Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Unformatted text preview: 234 10.2 Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 10.3 The Integral Test . . . . . . . . . . . . . . . . . . . . . . . . 244 10.4 Alternating Series . . . . . . . . . . . . . . . . . . . . . . . . 249 10.5 Comparison Tests . . . . . . . . . . . . . . . . . . . . . . . . 251 10.6 Absolute Convergence . . . . . . . . . . . . . . . . . . . . . 254 10.7 The Ratio and Root Tests . . . . . . . . . . . . . . . . . . . 256 10.8 Power Series . . . . . . . . . . . . . . . . . . . . . . . . . . 259 10.9 Calculus with Power Series . . . . . . . . . . . . . . . . . . . 261 10.10 Taylor Series . . . . . . . . . . . . . . . . . . . . . . . . . . 263 10.11 Taylor’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . 267 10.12 Additional exercises . . . . . . . . . . . . . . . . . . . . . . . 271...
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