MATH 2415-301 Exam II Review Problems 1. Find parametric equations for the tangent line to the curve with parametric e = t cos t, y = t, z = tsint; (T, T, 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 + (sint)j+tk. particle that moves along the 4. Find the velocity, speed, and acceleration of a t t (t) (2 sin)i+(2 cos )j at t 2 5. Find the unit tangent and the principal unit normal vectors for the h (2 cos t) i+(2 sin t) j+tk. r(t) 6. Find the curvature of r(t) = ti+ t2j + t k. 7. Find the curvature of the plane y = cos(r) + e2 at r 0. 8. Find the maximum curvature of y In x. hac cunvedune, hec eluriv 9. Find the tangential component ar and normal component aN for the cu r(t) 3ti tj+tk. 10. Let a(t) 2t i + e'j+ cos (t) k denote the acceleration of a moving pa i+2j- k, find the particle's velocity v(t) at any time t. v(0) M (a) Find the domain of f(x, y) V2- In(-1) (b) Sketch the graph of f(x, y) =6-x-2y.
MATH 2415-301 Exam II Review Problems 1. Find parametric equations for the tangent line to the curve with parametric e = t cos t, y = t, z = tsint; (T, T, 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 + (sint)j+tk. particle that moves along the 4. Find the velocity, speed, and acceleration of a t t (t) (2 sin)i+(2 cos )j at t 2 5. Find the unit tangent and the principal unit normal vectors for the h (2 cos t) i+(2 sin t) j+tk. r(t) 6. Find the curvature of r(t) = ti+ t2j + t k. 7. Find the curvature of the plane y = cos(r) + e2 at r 0. 8. Find the maximum curvature of y In x. hac cunvedune, hec eluriv 9. Find the tangential component ar and normal component aN for the cu r(t) 3ti tj+tk. 10. Let a(t) 2t i + e'j+ cos (t) k denote the acceleration of a moving pa i+2j- k, find the particle's velocity v(t) at any time t. v(0) M (a) Find the domain of f(x, y) V2- In(-1) (b) Sketch the graph of f(x, y) =6-x-2y.
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter8: Polar Coordinates And Parametric Equations
Section8.FOM: Focus On Modeling: The Path Of A Projectile
Problem 7P: Shooting into the Wind Using the parametric equations you derived in Problem 6. draw graphs of the...
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