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Unformatted text preview: MAC 2313, Fall 2010 — Midterm 2 Review Problems 1 We will discuss these problems in class on Friday 10/1 and Monday 10/4. Solutions will be posted on the course webpage over the weekend. 1 Find a vector function that represents the curve of intersection of the cylinder x 2 + y 2 = 16 and the plane x + z = 5. 2 A particle moves with position function r ( t ) = t ln t i + t j + e − t k . Find the velocity, acceleration, and speed of the particle. 3 Compute the position vector for a particle which passes through the origin at time t = 0 and has velocity vector v ( t ) = 2 t i + sin t j + cos t k . 4 Find the arc length of the curve r ( t ) = cos 3 t j + sin 3 t k from t = 0 to t = 1. 5 Consider the curve defined by r ( t ) = ( 4sin ct, 3 ct, 4cos ct ) . What value of c makes the arc length of the curve traced by r ( t ), for 0 ≤ t ≤ 1, equal to 10? 6 Show that if a particle moves at constant speed, then its velocity and acceleration vectors are orthogonal. Note that moving at constant speed doesare orthogonal....
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This note was uploaded on 12/10/2011 for the course MAC 2313 taught by Professor Keeran during the Fall '08 term at University of Florida.
- Fall '08