   Chapter 10.1, Problem 2E

Chapter
Section
Textbook Problem

# 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. x = t3 + t, y = t2 + 2, −2 ≤ t ≤ 2

To determine

To plot: The curve using the parametric equations. x=t3+t and y=t2+2 .

Explanation

Given data:

The parametric equation for the variable x is as follows.

x=t3+t (1)

The parametric equation for the variable y is as follows.

y=t2+2 (2)

The range of t is 2 to 2 .

Calculation:

The value of t is increased from 2 to 2 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 2 for t in the Equation (1).

x=t3+tx=(2)3+(2)=82x=10

Substitute 2 for t in the Equation (2)

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