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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

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BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

Find parametric equations for the path of a particle that moves along the circle x2 + (y − 1)2 = 4 in the manner described.

  1. (a) Once around clockwise, starting at (2, 1)
  2. (b) Three times around counterclockwise, starting at (2, 1)
  3. (c) Halfway around counterclockwise, starting at (0, 3)

(a)

To determine

To obtain: Clockwise orientation starting at (2,1) .

Explanation

Given data:

To obtain the clockwise position the equation y=1+2sint can be changed to

y=12sint

The parametric equation for the variable x is as follows.

x=2cost (1)

The parametric equation for the variable y is as follows.

y=12sint (2)

The range of t is 0 to 2π .

Calculation:

The value of t is increased from 0 to 2π and substituted in the parametric equations (1) and (2) to obtain the value of x and y respectively.

Substitute 0 for t in equation (1),

x=2cost=2cos(0)x=2

Substitute 0<

(b)

To determine

To obtain: Three times around counter clockwise orientation starting at (2,1) .

(c)

To determine

To plot: Halfway around counterclockwise string at (0,3) .

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P-52RECh-10 P-53RECh-10 P-54RECh-10 P-55RECh-10 P-56RECh-10 P-57RECh-10 P-58RECh-10 P-1PCh-10 P-2PCh-10 P-3PCh-10 P-4PCh-10 P-5PCh-10 P-6P

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