   Chapter 10.1, Problem 4E

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.4. x = e−t + t, y = et − t, −2 ≤ t ≤ 2

To determine

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

Explanation

Given data:

The parametric equation for the variable x is as follows.

x=et+t (1)

The parametric equation for the variable y is as follows.

y=ett (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=et+t=e(2)+(2)=7.392x=5.39

Substitute 2 for t in Equation (2).

y=et(2)=e2(2)=0

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