Exam II Formula Review Math 32A The midterm will test your understanding of the con-cepts underlying these formulas. As a ﬁrst step in your exam preparation, memorize the answers to each of these questions. You must do challenging problems in prepara-tion for the exam; this handout should only supplement other review materials. 1. Intrinsic properties of curves. Given a diﬀeren-tiable curve r ( t ), provide expressions for the follow-ing quantities. If a quantity is listed twice, provide two diﬀerent equations. • v ( t ) = • v ( t ) = • T ( t ) = • N ( t ) = • κ ( t ) = • κ ( t ) = 2. Motion in three-space. Given a curve r ( t ), relate r ( t ), v ( t ), and a ( t ). Use only the terms provided. Hint: where appropriate, use the fundamental the-orem of calculus. • Write v ( t ) in terms of r ( t ). • Write a ( t ) in terms of r ( t ). • Write v ( t ) in terms of a ( t ) and v0 = v ( t0 ). • Write
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