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265Lesson06Problems - problem Be sure to check that the...

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MATH 265: MULTIVARIABLE CALCULUS: LESSON 6 PROBLEMS Problems are worth 20 points each. (1) Determine the length of the curve -→ r ( t ) = e t cos t -→ ı + e t sin t -→ + e t -→ k for 0 t 1. (2) Determine the speed of a moving particle at time t = π 2 whose position at time t is given by the vector equation -→ r ( t ) = h sin 2 t, cos 3 t, cos 2 t i . (3) Calculate κ ( t ) for the curve given by -→ r ( t ) = t -→ ı + -→ + e t -→ k . (4) Determine the point on the plane curve f ( x ) = ln x where the curvature is max- imum. You may need to review max-min methods from Calculus I to do this
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Unformatted text preview: problem. Be sure to check that the curvature is max at the critical point. (5) Calculate the velocity and acceleration vectors and the speed at t = π 4 for a particle whose position at time t is given by-→ r ( t ) = cos t-→ ı + cos 2 t-→ + cos 3 t-→ k . (6) (Bonus question: worth 10 points. Total points for assignment not to exceed 100.) Find a formula for the curvature of the cycloid given by x = t-sin t,y = 1-cos t . 1...
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