Assignment 2(1).pdf - MATH 223 Assignment 2 Fall 2019 The assignment is not due However you are STRONGLY recommended to solve all the questions before

Assignment 2(1).pdf - MATH 223 Assignment 2 Fall 2019 The...

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MATH 223 Assignment 2 Fall 2019 The assignment is not due. However, you are STRONGLY recommended to solve all the questions before the coming quiz on next Monday. This assignment covers the materials from Sections 11.4. 1. Suppose that a space curve, C , is given by the vector-valued function r ( t ) = cos 3 t i + sin 3 t j + cos 2 t k , 0 t π/ 2 . Find the unit tangent vector to the curve at the point r ( t ). Then, up to three decimals, calculate the same vector when t = 1 . 113. 2. Consider the same space curve in Question 1. (a) Re-parametrize the curve in the same orientation in terms of the arc length, s , for 0 s 5 / 2. (b) Find the unit tangent vector to the curve at the point r ( s ). (c) Verify that v ( s ) = 1. Useful identities: sin 2 t + cos 2 t = 1, sin 2 t = 1 2 (1 - cos 2 t ). 3. Consider that a particle that moves in a plane along a curve, C , according to the vector-valued function r ( t ) = cos( t 2 ) i + sin( t 2 ) j . (a) Calculate the curvature κ ( s ) and the radius of curvature ρ ( s ). (b) Use your results found in (a) to describe
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