Chapter 12
Vector-Valued Functions
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Definition of Vector-Valued Function
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Figure 12.1
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Definition of the Limit of a Vector-Valued Function
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Figure 12.6
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Definition of Continuity of a Vector-Valued Function
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Definition of the Derivative of a Vector-Valued Function
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Figure 12.8
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Theorem 12.1 Differentiation of Vector-Valued Functions
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Theorem 12.2 Properties of the Derivative
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Definition of Integration of Vector-Valued Functions
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Figure 12.10
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Definitions of Velocity and Acceleration
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Figure 12.16
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Theorem 12.3 Position Function for a Projectile
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Definition of Unit Tangent Vector
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Definition of Principal Unit Normal Vector
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Figure 12.22
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Theorem 12.4 Acceleration Vector
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Theorem 12.5 Tangential and Normal Components of Acceleration
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Figure 12.24
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Theorem 12.6 Arc Length of a Space Curve
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Definition of Arc Length Function and Figure 12.29
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Theorem 12.7 Arc Length Parameter
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Figure 12.31
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Figure 12.32
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Definition of Curvature
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Theorem 12.8 Formulas for Curvature
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Figure 12.34
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Theorem 12.9 Curvature in Rectangular Coordinates
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Figure 12.35
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Figure 12.37
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Theorem 12.10 Acceleration, Speed, and Curvature
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Figure 12.38
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Summary of Velocity, Acceleration, and Curvature