Calculus
7th Edition
ISBN: 9781524916817
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 10, Problem 52SP
To determine
To find: the tangential, normal components of acceleration,and the curvature
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8. For the curve given by r(t) = (2 cos(t), 2 sin(t), 2t +), find
(a) the unit tangent vector
(b) the unit normal vector
(c) the unit binormal vector
(d) the curvature.
2. The parametric equations of a curve is x = 3 sint, y = 3 cost and z= = 4.
(a) Sketch the curve r(t) for 0 ≤ t ≤ 2π.
(b) Find the followings when t = 0:
(i) The unit tangent vector, T.
(ii) The principal unit normal, N.
2. The parametric equations of a curve is x = 3 sin t, y = 3 cost and z = 4.
(a) Sketch the curve r(t) for 0
Chapter 10 Solutions
Calculus
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- Force Repeat Problem 43 for a 25.0-pound weight and a bench inclined at 12.5.arrow_forward4. Consider the following curve 7 (t) = (-2 sin(t), – V5, 2 cos(t)) (a) Find the unit tangent vector. (b) - Find the curvature.arrow_forwardQuestion 13 Find the center of curvature of the curve y= Inx at (1, 0). (A) (4, 3) B) (3, 4) © (3, -2) D) (-2, 3)arrow_forward
- Problem 7. Consider the curve parametrized by r(t) = (3t², 2t³), t € [0, √3]. (a) Find the unit tangent vector T(t). (b) Find the length of the curve.arrow_forwardProblem 3. If ř(t) = (t,sint,cost), find 1. The domain of the given vector function? 2. Evaluate tangent vector of ř(1)?arrow_forward1. An object starts from rest at point P(1, 2, 0) and moves with an acceleration of a(t) = 3 + 2k. Find the location of the object after t = 2 seconds of movement. 2. Find the unit tangent vector T for the curve (t) = (t cos t, t sin t).arrow_forward
- Problem 2) Let ř(t) = . Find the unit tangent vector, unit normal vector, and curvature, 2 and unit binormal vector at t 0.arrow_forward8. For the curve given by r(t) = (sin³ t, cos3 t, sin² t), 0 ≤ t ≤, Find an equation for each (a) the unit tangent vector (b) the unit normal vector (c) the unit binormal vector (d) the curvaturearrow_forward
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