Spring 2007 - Linshaw's Class - Quiz 2 - Name: TA: Math...

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Name:PID:TA:Sec. No:Sec. Time:Math 20C.Quiz 2April 20, 20071. Find parametric equations for the tangent line to the curve given by
r(t) =t5i+t4j+t3k,at the point (1,1,1).Solution:Note thatr(1) = (1,1,1).We haver(t) = 5t4i+ 4t3j+ 3t2k, sor(1) =5i+ 4j+ 3k.The tangent line passes through (1,1,1) and is parallel to the vector5i+ 4j+ 3k. We can parametrize this line as follows:x= 1 + 5t,y= 1 + 4t,x= 1 + 3t.2. Find the position functionr(t) of a particle whose acceleration isa(t) =ti+t2j+ cos 2tk,which satisfies the initial conditionsv(0) =i+k, andr(0) =j.Solution: Integratinga(t) yieldsv(t) =t22i+t33j+12sin 2tk+C1,where
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Term
Spring
Professor
Helton
Tags
Equations, Vector Space, Parametric Equations, Constant of integration, Parametric equation

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