265Lesson05Problems

265Lesson05Problems - If a particle moving along a curved...

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MATH 265: MULTIVARIABLE CALCULUS: LESSON 5 PROBLEMS Problems are worth 20 points each. (1) Find a parametrization of the circle with center (1 , 3 , 5) and radius 3 in a plane parallel to the xy -plane. (2) Sketch the curve given by the vector valued function -→ r ( t ) = t 2 -→ ı + t 3 -→ , -∞ < t < . (3) Determine an equation for the line tangent to the curve -→ r ( t ) = h t sin t,t cos t,t i at the point ( π 2 , 0 , π 2 ) on the curve. (4) Compute Z 1 0 h t,e t ,te t i d t . (5) Compute lim t 0 ± cos t - 1 t 2 , e t - 1 t , sin t t ² . (You may need to review L’Hopital’s Rule to do this problem.) (6) (Bonus question: worth 10 points. Total points for assignment not to exceed 100.)
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Unformatted text preview: If a particle moving along a curved track (like a roller coaster) flies off the track, it continues in the direction of the tangent vector at the point where it left the track, at least if there are no external forces such as gravity or friction acting on it. Suppose a particle rolling down (towards the xy-plane) the helix shaped track given by-→ r ( t ) = h 2 cos t, 2 sin t,t i flies off the track when t = π 4 . Determine the point where the particle will hit the xy-plane. 1...
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This note was uploaded on 02/24/2011 for the course MATH 265 taught by Professor Jerrymetzger during the Winter '11 term at North Dakota.

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