Problem

Describe and sketch the surface. $ x^2 + z^2 =…

00:56

Question

Answered step-by-step

Problem 2 Easy Difficulty

(a) Sketch the graph of $ y = e^x $ as a curve in $ \mathbb{R}^2 $.
(b) Sketch the graph of $ y = e^x $ as a surface in $ \mathbb{R}^3 $.
(c) Describe and sketch the surface $ z = e^x $.

Video Answer

Solved by verified expert

Textbook Answer

Official textbook answer

Video by Carson Merrill

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Top Calculus 3 Educators

Watch More Solved Questions in Chapter 12

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42

Problem 43

Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Problem 49

Problem 50

Problem 51

Problem 52

Problem 53

Video Transcript

Okay, So what we see here is we first want to start by graphing. Why equals e to the X and we want to do it just in the are too. So that's the plane. Just that just involves X and y. So this is the graph that we see Onda were pretty familiar with the graph of y equals e to the X Because it's this typical exponential equation. Then we go into three dimensions and we want to know Well, what does it look like if we have y equals e to the X in this dimension in three dimensions? What we see it follows a very similar curve. If we were to just make this flat, it looks like the exact same curve that we saw before. Um, it would look something like this. However, the difference is if we move about in the third dimension, we see that it has a depth that goes as faras egos. So no matter what Z is, we have this y equals e to the X shape of the graph. But then it also has a third dimension that z next. What we want to dio is graph y equal actually easy equals. Eat the X So me grab Z equals easy X. We're going to see something very similar. Um, the only difference is now, instead of the width of the graph being related Thio Z Now the width of the graph is related to why is we see, no matter how far, why goes we have this e to the X looking graph, but in this case it's a function of Z, which is why it's going up here going down here. This is changing in with regards to Z as X increases or decreases, and then the width of the graph is a result of why.

Get More Help with this Textbook

James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups

Study with other students and unlock Numerade solutions for free.

Problem

Describe and sketch the surface. $ x^2 + z^2 =…

This textbook answer is only visible when subscribed! Please subscribe to view the answer

More Answers

Related Courses

Calculus: Early Transcendentals

Related Topics

Discussion

Top Calculus 3 Educators

Catherine Ross

Anna Marie Vagnozzi

Heather Zimmers

Michael Jacobsen

Calculus 3 Courses

Recommended Videos

Watch More Solved Questions in Chapter 12

Video Transcript

James Stewart

Calculus: Early Transcendentals

Catherine Ross

Anna Marie Vagnozzi

Heather Zimmers

Michael Jacobsen

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Calculus: Early Transcendentals

Catherine Ross

Anna Marie Vagnozzi

Heather Zimmers

Michael Jacobsen

James StewartCalculus: Early Transcendentals

Catherine Ross

Anna Marie Vagnozzi

Heather Zimmers

Michael Jacobsen

James Stewart

Calculus: Early Transcendentals