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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

Determine whether the points P and Q lie on the given surface.

1. r(u, v) = ⟨u + v, u − 2v, 3 + uvP(4, −5, 1), Q(0, 4, 6)

To determine

Whether the point P(4,5,1) lies on the surface r(u,v)=u+v,u2v,3+uv or not and whether the point Q(0,4,6) lies on the surface r(u,v)=u+v,u2v,3+uv or not.

Explanation

Given data:

The surface vector is r(u,v)=u+v,u2v,3+uv and the point is P(4,5,1) .

The surface vector is r(u,v)=u+v,u2v,3+uv and the point is Q(0,4,6) .

The point P(4,5,1) lies on the surface r(u,v)=u+v,u2v,3+uv if and only if there are values for u and v such that the corresponding values of u and v must satisfy the vector r(u,v)=u+v,u2v,3+uv .

Equate x-, y-, and z-coordinates of the point to the corresponding points of the vector r(u,v) and obtain the values of u and v as follows.

u+v=4 (1)

u2v=5 (2)

3+uv=1 (3)

Rearrange the equation (1).

u=4v

Substitute 4v for u in equation (2),

(4v)2v=543v=53v=9v=3

Substitute 3 for v in the expression u=4v ,

u=43=1

Substitute 1 for u and 3 for v in equation (3),

3+13=11=1

The values of u and v are satisfied for the vector r(u,v)

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Chapter 16 Solutions

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Sect-16.1 P-11ESect-16.1 P-12ESect-16.1 P-13ESect-16.1 P-14ESect-16.1 P-15ESect-16.1 P-16ESect-16.1 P-17ESect-16.1 P-18ESect-16.1 P-21ESect-16.1 P-22ESect-16.1 P-23ESect-16.1 P-24ESect-16.1 P-25ESect-16.1 P-26ESect-16.1 P-29ESect-16.1 P-30ESect-16.1 P-31ESect-16.1 P-32ESect-16.1 P-33ESect-16.1 P-34ESect-16.1 P-35ESect-16.1 P-36ESect-16.2 P-1ESect-16.2 P-2ESect-16.2 P-3ESect-16.2 P-4ESect-16.2 P-5ESect-16.2 P-6ESect-16.2 P-7ESect-16.2 P-8ESect-16.2 P-9ESect-16.2 P-10ESect-16.2 P-11ESect-16.2 P-12ESect-16.2 P-13ESect-16.2 P-14ESect-16.2 P-15ESect-16.2 P-16ESect-16.2 P-17ESect-16.2 P-18ESect-16.2 P-19ESect-16.2 P-20ESect-16.2 P-21ESect-16.2 P-22ESect-16.2 P-23ESect-16.2 P-24ESect-16.2 P-25ESect-16.2 P-26ESect-16.2 P-31ESect-16.2 P-32ESect-16.2 P-33ESect-16.2 P-34ESect-16.2 P-35ESect-16.2 P-36ESect-16.2 P-37ESect-16.2 P-38ESect-16.2 P-39ESect-16.2 P-40ESect-16.2 P-41ESect-16.2 P-42ESect-16.2 P-43ESect-16.2 P-44ESect-16.2 P-45ESect-16.2 P-46ESect-16.2 P-47ESect-16.2 P-48ESect-16.2 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P-6RECh-16 P-7RECh-16 P-8RECh-16 P-9RECh-16 P-10RECh-16 P-11RECh-16 P-12RECh-16 P-13RECh-16 P-14RECh-16 P-15RECh-16 P-16RECh-16 P-17RECh-16 P-18RECh-16 P-19RECh-16 P-20RECh-16 P-21RECh-16 P-22RECh-16 P-23RECh-16 P-24RECh-16 P-25RECh-16 P-27RECh-16 P-28RECh-16 P-29RECh-16 P-30RECh-16 P-31RECh-16 P-32RECh-16 P-33RECh-16 P-34RECh-16 P-35RECh-16 P-36RECh-16 P-37RECh-16 P-38RECh-16 P-39RECh-16 P-40RECh-16 P-41RECh-16 P-1PCh-16 P-2PCh-16 P-3PCh-16 P-5PCh-16 P-6P

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