Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 14: Partial Derivatives - Section 14.6 - Tangent Planes and Differentials - Exercises 14.6 - Page 833: 5


a) $2x+ 2y+z=4$; b) $x=0+2t=2t,y=1+2t; z=2+t$

Work Step by Step

a. The vector equation is given as: $r(x,y,z)=r_0+t \nabla f(r_0)$ The equation of tangent line is given by $\nabla f(0,1,2)=\lt 2,2,1 \gt$ Now, $(2)(x-0)+(2)(y-1)+(1)(z-2)=0 \implies 2x+ 2y+z=4$ b. The vector equation is given as: $r=r_0+t \nabla f(r_0)$ The parametric equations are: $x=0+2t=2t,y=1+2t; z=2t$ Thus, $x=2t,y=1+2t; z=2+t$
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