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Chapter 10.1, Problem 1E

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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

Solutions

Chapter
Section
BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
To determine

To plot: The curve using the parametric equations x=1t2 and y=2tt2 .

Answer

The curve representing the parametric equations x=1t2 and y=2tt2 is shown in Figure 1.

Explanation

Given data:

The parametric equation for the variable x is as follows.

x=1t2 (1)

The parametric equation for the variable y is as follows.

y=2tt2 (2)

The range of t is 1 to 2 .

Calculation:

The value of t is increased from 1 to 2 with a step value of 1 and substituted in the Equations (1) and (2) to obtain the value of x and y respectively.

Substitute 1 for t in the Equation (1).

x=1(1)2=11x=0

Substitute 1 for t in the Equation (2).

y=2tt2=2(1)(1)2=21y=3

The values of x and y for each step value of t is tabulated in the below table.

t x y
1 0 3
0 1 0
1 0 1
2 3 0

Graph:

Plot the curve with the points (x,y) obtained by the different values of t as shown in Figure 1.

images

The curve is traced as t increases from 1 to 2.

The graph obtained from the parametric equations for the variables x and y forms a parabolic curve. The arrowhead in the Figure 1 indicates the direction of the increasing values of t .

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