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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

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Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
Textbook Problem

  1. (a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases.
  2. (b) Eliminate the parameter to find a Cartesian equation of the curve.

7. x = t2 − 3, y = t + 2, −3 ≤ t ≤ 3

(a)

To determine

To plot: The curve using the parametric equations. x=t23 and y=t+2 .

Explanation

Given data:

The parametric equation for the variable x is as follows.

x=t23 (1)

The parametric equation for the variable y is as follows.

y=t+2 (2)

The range of t is 3 to 3 .

Calculation:

The value of t is increased from 3 to 3 with a step value of 1 and substituted in the parametric Equations (1) and (2) to obtain the value of x and y respectively.

Substitute 3 for t in Equation (1).

x=t23=(3)23=93x=6

Substitute 3 for t in Equation (2).

y=t+2=(3)+2y=1

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

(b)

To determine

To find: obtain a Cartesian equation of the curve by eliminating parameter t .

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