Exam 2 Study Guide
Exam 2 Study Guide MTH 203
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This 5 page Study Guide was uploaded by Cal_Vez21 on Tuesday March 1, 2016. The Study Guide belongs to MTH 203 at Grand Valley State University taught by Dr. Firas Hindeleh in Winter 2016. Since its upload, it has received 21 views. For similar materials see Calculus 3 in Mathematics (M) at Grand Valley State University.
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Date Created: 03/01/16
Exam 2 Study Guide MTH 203-02 – Dr. Firas Hindeleh By Caleb Alves Topics Covered: Parametrization of circles Vector functions and Space curves Derivatives and Integrals of vector functions Arc Length and Curvature Motion in 3D Spherical Coordinates Parametrizing surfaces Limits of Surfaces 2 2 2 Recall the equation of a circle with radius 1 is: x +y +z =1 2 2 1) Now parametrize the intersection of the cylinder (x−2 )+ (y−1 )=2 and the x+y+2z=1 plane . Page 1 2) Find a vector function for the line segment that joins the points P (1, 1, 3) and Q (-1, 1, -1). 2 1 3) Find the tangent vector to the space curve: r(t=¿t −1, cot t)>¿ at t = 2. Then, find the normal and bi-normal vectors at the same point. Page 2 4) For the space curve in the previous problem, calculate the arc length and curvature between the t = -2 and t = 2. 5) A sailboat leaves a marina headino east with a velocity of 16 m/s. The wind is headed NNE, at an angle 60 above the horizontal, and applies a constant force of 5 N to the boat, which causes it to accelerate at a rate a(t=¿t+1,t ,0>. Calculate the position and speed of the boat at t = 20s. 6) Convert the vector function r(t=¿8t ,t−1,cos (2t)>¿ to spherical coordinates. Then, describe the surface it creates. Page 3 2cos(x)+y 7) Find the limit of the function z(x ,y= 2 2 at the origin. x +y Page 4 1 8) Rotate the function y= 2in 2( +) around the x-axis from x = 0 to x = 2, then parametrize the surface it creates. Page 5
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