MATH 2415-301 Exam II -Review Problems 1. Find parametric equations for the tangent line to the curve with parametric equations t cos t, y t, z = tsin t; (T, TT, 0) 2. Find the arc length of r(t) i+ tj+ 2tk on [1, 2]. 3. Find the arc lenght of one turn of the helix r (t) (cos t) i+ (sin t)j+tk 4. Find the velocity, speed, and acceleration of a particle that moves along the plane curve C given by t t COS TT (t) (2 sin)i+ (2 cos)j at t= 2 5. Find the unit tangent and the principal unit normal vectors for the helix given by r(t) (2 cos t) i+(2 sin t) j+ tk. 6. Find the curvature of r(t) = ti + t2j+ t k. at r 0. 7. Find the curvature of the plane y = -cos() + e 8. Find the maximum curvature of y In r. hack cunrerune, chece cleiratine+cet clunvahve to 2ors 9. Find the tangential component aT and normal component aN for the curve given by C 3ti tj+tk. r(t) w 10. Let a(t) 2t i + ej + cos(t) k denote the acceleration of a moving particle. If the initial velo v(0) i+2j k, find the particle's velocity v(t) at any time t. (a) Find the domain of f(x, y) = In2-1) H. (b) Sketch the graph of f(r, y) 6-x-2y. 12. Find the limit of show it does not exists. (a) 4 lim (r,y)(0,0) 2ys (b) xy y lim (ay)(1,0) (x 1)2 +y

MATH 2415-301 Exam II -Review Problems 1. Find parametric equations for the tangent line to the curve with parametric equations t cos t, y t, z = tsin t; (T, TT, 0) 2. Find the arc length of r(t) i+ tj+ 2tk on [1, 2]. 3. Find the arc lenght of one turn of the helix r (t) (cos t) i+ (sin t)j+tk 4. Find the velocity, speed, and acceleration of a particle that moves along the plane curve C given by t t COS TT (t) (2 sin)i+ (2 cos)j at t= 2 5. Find the unit tangent and the principal unit normal vectors for the helix given by r(t) (2 cos t) i+(2 sin t) j+ tk. 6. Find the curvature of r(t) = ti + t2j+ t k. at r 0. 7. Find the curvature of the plane y = -cos() + e 8. Find the maximum curvature of y In r. hack cunrerune, chece cleiratine+cet clunvahve to 2ors 9. Find the tangential component aT and normal component aN for the curve given by C 3ti tj+tk. r(t) w 10. Let a(t) 2t i + ej + cos(t) k denote the acceleration of a moving particle. If the initial velo v(0) i+2j k, find the particle's velocity v(t) at any time t. (a) Find the domain of f(x, y) = In2-1) H. (b) Sketch the graph of f(r, y) 6-x-2y. 12. Find the limit of show it does not exists. (a) 4 lim (r,y)(0,0) 2ys (b) xy y lim (ay)(1,0) (x 1)2 +y

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.4: Plane Curves And Parametric Equations

Problem 53E

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