Assignment 3.pdf - MATH 223 Assignment 3 Fall 2019 The assignment is not due However you are STRONGLY recommended to solve all the questions before the

Assignment 3.pdf - MATH 223 Assignment 3 Fall 2019 The...

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MATH 223 Assignment 3 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 11.5, 12.1, 12.2, a part of 12.3. 1. Suppose that a space curve, C , is given by the vector-valued function r ( t ) = e t i + 2 t j + e - t k . (a) Calculate the velocity, speed, acceleration, curvature, and torsion at time t = 0. (b) Find the normal and tangential acceleration of the curve at time t = 0 in two ways: i. by calculating the dot product of the acceleration vector with the unit normal vector and with the unit tangent vector, respectively ii. by calculating the rate of change of the speed and the centripetal acceleration obtained from the speed and the radius of curvature. 2. Find the domain of the following functions. Then, calculate the value of the function at the indicated point(s): (a) f ( x, y ) = - xy , points: (-0.162, 2.333) and (1.032, -0.546) (b) g ( x, y ) = 3 9 - x 2 - y 2 , point: (0,0) and (5, 4) (c) h ( x, y ) = | x | (d) k ( x, y ) = sin 1 x + y (e) l ( x, y ) = 16 - x 2 - y 2 3. Sketch the graphs of the functions in (c) and (e). Also, show the level curves of the function in
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