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Chapter 10: Q. 43 (page 695)

In Problems 43 and 44, the parametric equations of four curves are given. Graph each of them, indicating the orientation.

C1:x=t,y=t2,-4鈮�t鈮�4C2:x=cost,y=1-sin2t,0鈮�t鈮�蟺C3:x=et,y=e2t,0鈮�t鈮�ln4C4:x=t,y=t,0鈮�t鈮�16

Short Answer

Expert verified

The graph of each figure is shown in respective figures.

Step by step solution

01

Step 1. Given Information

The given parametric equations are

C1:x=t,y=t2,-4鈮�t鈮�4C2:x=cost,y=1-sin2t,0鈮�t鈮�蟺C3:x=et,y=e2t,0鈮�t鈮�ln4C4:x=t,y=t,0鈮�t鈮�16

02

Step 2. Graph of C1

We have x=t2,y=t2,-4鈮�t鈮�4

The coordinates of ordered pairs are -4,16,-2,4,0,0,2,4,4,16.

Plot these points on the plane and join them to obtain the graph

03

Step 3. Graph of C2

We have x=cost,y=1-sin2t,0鈮�t鈮�蟺

The coordinates are 1,1,22,12,0,0,-22,12,-1,1

Plot these points on the plane and join them to obtain the graph

04

Step 4. Graph of C3

We have x=et,y=e2t,0鈮�t鈮�ln4

The coordinates are 1,1,2,4,3,9,4,16

Plot these points on the plane and join them to obtain the graph

05

Step 5. Graph of C5

We have x=t,y=t,0鈮�t鈮�16

The coordinates are 0,0,2,4,22,8,23,12,4,16

Plot these points on the plane and join them to obtain the graph

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