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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
Textbook Problem

Match the graphs of the parametric equations x = f(t) and y = g(t) in (a)–(d) with the parametric curves labeled I–IV. Give reasons for your choices.

  1. (a) images
  2. (b) images
  3. (c) images
  4. (d) images

To determine

To match: The parametric equations x=f(t) and y=g(t) shown in graphs (a) to (d) with the parametric curves labeled I to IV.

Explanation

The parametric equations x=f(t) and y=g(t) shown in graph (a) matches with the parametric curve labeled III.

The parametric equations x=f(t) and y=g(t) shown in graph (b) matches with the parametric curve labeled I.

The parametric equations x=f(t) and y=g(t) shown in graph (c) matches with the parametric curve labeled IV.

The parametric equations x=f(t) and y=g(t) shown in graph (d) matches with the parametric curve labeled II.

Given:

The parametric equation for the variable x is as follows.

x=f(t)

The parametric equation for the variable y is as follows.

y=g(t)

Calculation:

Graph (a):

From graph (a), it is observed that the parameter x varies from (1x2) at the interval of (0t1) and parameter y varies from (1y1) at the interval of (0t1)

Plot the parametric curve for which the parameter x varies from (1x2) and y varies from (1y1) as shown below in Figure 1.

The parametric curve shown in Figure 1 resembles the parametric curve shown in graph–III. Therefore, the parametric equations x=f(t) and y=g(t) shown in graph (a) matches with the parametric curve labeled III.

Graph (b):

From graph (b), it is observed that the parameter x varies four times periodically from (2x2) at the interval of (0t1) and parameter y also varies six times periodically from (2y2) at the interval of (0t1) .

Plot the parametric curve for which the parameter x varies from (2x2) and y varies from (2y2) as shown below in Figure 2

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Sect-10.1 P-11ESect-10.1 P-12ESect-10.1 P-13ESect-10.1 P-14ESect-10.1 P-15ESect-10.1 P-16ESect-10.1 P-17ESect-10.1 P-18ESect-10.1 P-19ESect-10.1 P-20ESect-10.1 P-21ESect-10.1 P-22ESect-10.1 P-23ESect-10.1 P-24ESect-10.1 P-25ESect-10.1 P-26ESect-10.1 P-27ESect-10.1 P-28ESect-10.1 P-29ESect-10.1 P-30ESect-10.1 P-31ESect-10.1 P-32ESect-10.1 P-33ESect-10.1 P-34ESect-10.1 P-35ESect-10.1 P-36ESect-10.1 P-37ESect-10.1 P-38ESect-10.1 P-39ESect-10.1 P-40ESect-10.1 P-41ESect-10.1 P-42ESect-10.1 P-43ESect-10.1 P-44ESect-10.1 P-45ESect-10.1 P-46ESect-10.1 P-47ESect-10.1 P-48ESect-10.1 P-49ESect-10.1 P-50ESect-10.1 P-51ESect-10.1 P-52ESect-10.2 P-1ESect-10.2 P-2ESect-10.2 P-3ESect-10.2 P-4ESect-10.2 P-5ESect-10.2 P-6ESect-10.2 P-7ESect-10.2 P-8ESect-10.2 P-9ESect-10.2 P-10ESect-10.2 P-11ESect-10.2 P-12ESect-10.2 P-13ESect-10.2 P-14ESect-10.2 P-15ESect-10.2 P-16ESect-10.2 P-17ESect-10.2 P-18ESect-10.2 P-19ESect-10.2 P-20ESect-10.2 P-21ESect-10.2 P-22ESect-10.2 P-23ESect-10.2 P-24ESect-10.2 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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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