Calculus Volume 3
Calculus Volume 3
16th Edition
ISBN: 9781938168079
Author: Gilbert Strang, Edwin Jed Herman
Publisher: OpenStax
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Chapter 3.4, Problem 193E

For each of the following problems, find the tangential and normal components of acceleration.

193. r ( t ) = 3 cos ( 2 π t ) i + 3 sin ( 2 π t ) j

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Chapter 3 Solutions

Calculus Volume 3

Ch. 3.1 - Give the component functions x=f(t) and y=g(t) for...Ch. 3.1 - Given r(t)=3secti+2tantj , find the following...Ch. 3.1 - Sketch the curve of the vector-valued function...Ch. 3.1 - Evaluate limt0eti+sinttj+etk .Ch. 3.1 - Given the vector-valued function r(t)=cost,sint ,...Ch. 3.1 - Given the vector-valued function r(t)=t,t2+1 ,...Ch. 3.1 - Let r(t)=eti+sintj+lntk . Find the following...Ch. 3.1 - Find the limit of the following vector-valued...Ch. 3.1 - Find the limit of the following vector-valued...Ch. 3.1 - Find the limit of the following vector-valued...
Ch. 3.1 - Find the limit of the following vector-valued...Ch. 3.1 - Find the limit of the following vector-valued...Ch. 3.1 - Find the limit of the following vector-valued...Ch. 3.1 - Find the limit of the following vector-valued...Ch. 3.1 - Find the domain of the vector-valued functions....Ch. 3.1 - Find the domain of the vector-valued functions....Ch. 3.1 - Find the domain of the vector-valued functions....Ch. 3.1 - Let r(t)=cost,t,sint and use it to answer the...Ch. 3.1 - Let r(t)=cost,t,sint and use it to answer the...Ch. 3.1 - Let r(t)=cost,t,sint and use it to answer the...Ch. 3.1 - Let r(t)=cost,t,sint and use it to answer the...Ch. 3.1 - Eliminate the parameter t, write the equation in...Ch. 3.1 - Eliminate the parameter t, write the equation in...Ch. 3.1 - Eliminate the parameter t, write the equation in...Ch. 3.1 - Eliminate the parameter t, write the equation in...Ch. 3.1 - Eliminate the parameter t, write the equation in...Ch. 3.1 - Use a graphing utility to sketch each of the...Ch. 3.1 - Use a graphing utility to sketch each of the...Ch. 3.1 - Use a graphing utility to sketch each of the...Ch. 3.1 - Use a graphing utility to sketch each of the...Ch. 3.1 - Use a graphing utility to sketch each of the...Ch. 3.1 - Use a graphing utility to sketch each of the...Ch. 3.1 - Use a graphing utility to sketch each of the...Ch. 3.1 - Use a graphing utility to sketch each of the...Ch. 3.1 - Use a graphing utility to sketch each of the...Ch. 3.1 - Use a graphing utility to sketch each of the...Ch. 3.1 - [T] Let r(t)=costi+sintj+0.3sin(2t)k . Use...Ch. 3.1 - [T] Use the result of the preceding problem to...Ch. 3.1 - Use the results If the preceding two problems to...Ch. 3.1 - a. Graph the curve...Ch. 3.2 - Compute the derivatives of the vector-valued...Ch. 3.2 - Compute the derivatives of the vector-valued...Ch. 3.2 - Compute the derivatives of the vector-valued...Ch. 3.2 - Compute the derivatives of the vector-valued...Ch. 3.2 - Compute the derivatives of the vector-valued...Ch. 3.2 - Compute the derivatives of the vector-valued...Ch. 3.2 - Compute the derivatives of the vector-valued...Ch. 3.2 - Compute the derivatives of the vector-valued...Ch. 3.2 - Compute the derivatives of the vector-valued...Ch. 3.2 - Compute the derivatives of the vector-valued...Ch. 3.2 - For the following problems, find a tangent vector...Ch. 3.2 - For the following problems, find a tangent vector...Ch. 3.2 - For the following problems, find a tangent vector...Ch. 3.2 - For the following problems, find a tangent vector...Ch. 3.2 - Find the unit tangent vector for the following...Ch. 3.2 - Find the unit tangent vector for the following...Ch. 3.2 - Find the unit tangent vector for the following...Ch. 3.2 - Find the unit tangent vector for the following...Ch. 3.2 - Find the following. 59. ddt[r(t2)]Ch. 3.2 - Find the following. 60. ddt[t2.s(t)]Ch. 3.2 - Find the following. 61. ddt[r(t).s(t)]Ch. 3.2 - Compute the first, second, and third derivatives...Ch. 3.2 - Find r(t)r(t) for r(t)=3t5i+5tj+2t2k .Ch. 3.2 - The acceleration function, initial velocity, and...Ch. 3.2 - The position vector of a particle is...Ch. 3.2 - Find the velocity and the speed of a panicle with...Ch. 3.2 - Find the velocity function and show that v(t) is...Ch. 3.2 - Show that the speed of the particle is...Ch. 3.2 - Evaluate ddt[u(t)u(t)] given u(t)=t2i2tj+k .Ch. 3.2 - Find the antiderivative of...Ch. 3.2 - Evaluate 03ti+t2jdt .Ch. 3.2 - An object starts from nest at point P(1,2,0) and...Ch. 3.2 - Show that if the speed 0f a particle traveling...Ch. 3.2 - Given r(t)=ti+3tj+t2k and u(t)=4ti+t2j+t3k , find...Ch. 3.2 - Given r(t)=t+cost,tsint , find the velocity and...Ch. 3.2 - Find the velocity vector for the function...Ch. 3.2 - Find the equation of the tangent line to the curve...Ch. 3.2 - Describe and sketch the curve represented by the...Ch. 3.2 - Locate the highest point on the curve r(t)=6t,6tt2...Ch. 3.2 - The position vector for a particle is...Ch. 3.2 - The position vector for a particle is...Ch. 3.2 - The position vector for a particle is...Ch. 3.2 - A particle travels along the path of a helix with...Ch. 3.2 - A particle travels along the path of a helix with...Ch. 3.2 - A particle travels along the path of a helix with...Ch. 3.2 - A particle travels along the path of a helix with...Ch. 3.2 - A particle travels along the path of an ellipse...Ch. 3.2 - A particle travels along the path of an ellipse...Ch. 3.2 - A particle travels along the path of an ellipse...Ch. 3.2 - Given the vector-valued function r(t)=tant,sect,0...Ch. 3.2 - Given the vector-valued function r(t)=tant,sect,0...Ch. 3.2 - Given the vector-valued function r(t)=tant,sect,0...Ch. 3.2 - Find the minimum speed of a particle traveling...Ch. 3.2 - Given r(t)=ti+2sintj+2costk and...Ch. 3.2 - Given r(t)=ti+2sintj+2costk and...Ch. 3.2 - Now, use the product rule for the derivative of...Ch. 3.2 - Find the unit tangent vector T(t) for the...Ch. 3.2 - Find the unit tangent vector T(t) for the...Ch. 3.2 - Find the unit tangent vector T(t) for the...Ch. 3.2 - Evaluate the following integrals: 100. ( e...Ch. 3.2 - Evaluate the following integrals: 101. 01r(t)dt ,...Ch. 3.3 - Find the arc length of the curve on the given...Ch. 3.3 - Find the arc length of the curve on the given...Ch. 3.3 - Find the arc length of the curve on the given...Ch. 3.3 - Find the arc length of the curve on the given...Ch. 3.3 - r(t)=etcost,etsint over the interval [0,2] . 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