   Chapter 10.2, Problem 36E

Chapter
Section
Textbook Problem

Comparing Plane Curves In Exercises 35-38. determine any differences between the curves of the parametric equations. Are the graphs the same? Are the orientations the same? Are the curves smooth? Explain.(a) x = t + 1 , y = t 3 (b) x = − t + 1 , y = ( − t ) 3

To determine

To calculate: Difference between curves of parametric equation

a) x=t+1.....(1)y=t3......(2)

b) x=t+1.....(1)y=(t)3......(2)

Are the graphs are same? Are orientation are same? Are same are curves are smooth?

Explanation

Given:

x=t+1.....(1)y=t3......(2)

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

Calculation:

The given equation are

x=t+1.....(1)y=t3......(2)

Solving these two equation we get

y=(x1)3

Graph is shown as below:

Differentiating (1) and (2) with respect to t

dxdt=1 and dydt=3t2

and slope will be dydx=dydtdxdt=3t21=3t2

From the slope it is clear that curve is not smooth

The given equation in (b) are

x=t+1

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