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.
$C_{1} : x = t, y = t^{2}, - 4 \leq t \leq 4 C_{2} : x = \cos t, y = 1 - \sin^{2} t, 0 \leq t \leq π C_{3} : x = e^{t}, y = e^{2 t}, 0 \leq t \leq \ln 4 C_{4} : x = \sqrt{t}, y = t, 0 \leq t \leq 16$

Short Answer

Expert verified

The graph of each figure is shown in respective figures.

Step by step solution

Step 1. Given Information

The given parametric equations are

$C_{1} : x = t, y = t^{2}, - 4 \leq t \leq 4 C_{2} : x = \cos t, y = 1 - \sin^{2} t, 0 \leq t \leq π C_{3} : x = e^{t}, y = e^{2 t}, 0 \leq t \leq \ln 4 C_{4} : x = \sqrt{t}, y = t, 0 \leq t \leq 16$

Step 2. Graph of C1

We have $x = t^{2}, y = t^{2}, - 4 \leq t \leq 4$

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

Step 3. Graph of C2

We have $x = \cos t, y = 1 - \sin^{2} t, 0 \leq t \leq π$

The coordinates are $(1, 1), (\frac{\sqrt{2}}{2}, \frac{1}{2}), (0, 0), (- \frac{\sqrt{2}}{2}, \frac{1}{2}), (- 1, 1)$

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

Step 4. Graph of C3

We have $x = e^{t}, y = e^{2 t}, 0 \leq t \leq \ln 4$

The coordinates are $(1, 1), (2, 4), (3, 9), (4, 16)$

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

Step 5. Graph of C5

We have $x = \sqrt{t}, y = t, 0 \leq t \leq 16$

The coordinates are $(0, 0), (2, 4), (2 \sqrt{2}, 8), (2 \sqrt{3}, 12), (4, 16)$

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

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Graph of C1

Step 3. Graph of C2

Step 4. Graph of C3

Step 5. Graph of C5

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Statistics

Decision Maths

Geometry

Logic and Functions

Probability and Statistics

Study anywhere. Anytime. Across all devices.

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≤t≤4C2:x=cost,y=1-sin2t,0≤t≤πC3:x=et,y=e2t,0≤t≤ln4C4:x=t,y=t,0≤t≤16

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Graph of C1

Step 3. Graph of C2

Step 4. Graph of C3

Step 5. Graph of C5

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Statistics

Decision Maths

Geometry

Logic and Functions

Probability and Statistics

Study anywhere. Anytime. Across all devices.