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mthsc206-fall-2010-exam-study-guide-02

# mthsc206-fall-2010-exam-study-guide-02 - Topics for Exam 2...

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Topics for Exam 2 2 Vector-valued functions and functions of several variables 2.1 Vector-valued Functions For r ( t ) = f ( t ) i + g ( t ) j + h ( t ) k , how do you compute (a) lim t a r ( t ); (b) r 0 ( t ); (c) Z b a r ( t ) dt ; (d) T ( t ); (e) N ( t ); (f) B ( t ); (g) κ ( t ). How do you compute the arc length of the curve C parameterized by the vector function r ( t ) on a t b ? How do you ﬁnd the radius of the circle of curvature at a point? How do you ﬁnd the equation of the circle of curvature at a point? What is ideal projectile motion? What are the parametrizations of this motion? 2.2 Functions of several variables How do you ﬁnd and graph the domain for a function of two variables? How do you ﬁnd and graph the domain for a function of three variables? In what space does the domain for a function f ( x,y ) reside? In what space does the range of f ( x,y ) reside? In what space does the graph of the function f ( x,y ) reside? In what space does the domain for a function
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