Question

Answered step-by-step

Problem 61 Hard Difficulty

(a) Graph the function $ f(x) = \sin x - \frac{1}{1000} \sin (1000x) $ in the viewing rectangle
$ [-2 \pi, 2 \pi] $ by $ [-4, 4] $. What slope does the graph appear to have at the origin?

(b) Zoom in to the viewing window $ [-0.4, 0.4] $ by $ [-0.25, 0.25] $ and estimate the value of $ f'(0) $. Does this agree with your answer from part (a)?

(c) Now zoom in to the viewing window $ [-0.008, 0.008] $ by $ [-0.005, 0.005] $. Do you wish to revise your estimate for $ f'(0) $?

Video Answer

Solved by verified expert

Textbook Answer

Official textbook answer

Video by Patrick Delos Reyes

Numerade Educator

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

Watch More Solved Questions in Chapter 2

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

Problem 54

Problem 55

Problem 56

Problem 57

Problem 58

Problem 59

Problem 60

Problem 61

Video Transcript

So here we are going to graph the function sign x minus Sign of 1000 X. All over 1000. And then observe it in different viewing rectangles. And Try to observe what the slope at zero is. So I've taken the first bounds -2 pi to pie And -4- four. Those are X and Y bounds respectively. And so it looks something like this here. I'm using Dismas but you can use your graphing calculator, your own graphing calculator or any other graphing utility you have. And so it looks like a zero. We have a pretty straight line that goes from negative one negative 1 to 1 comma one. So we can approximate the slope to be about one. So we're going to say the slope is about one. Now we have to change our bounds to these values. So I can do that in Desmond's here by using this graph settings button and changing the X axis bounds the ones we need and are Y axis bones similarly. And so now can see that it's a little different or you can see but it's not your typical sine function, there is a little bit of a squiggle going on and so line very close to the origin is kind of hard to see from here. Well assuming just a tiny bit and it looks like it goes flat just right where it hits the origin. So let's go ahead and approximate This answer. This slope as zero which of course does not agree with our answer from party. And then we're going to zoom in one last time here To negative 0.008 And positive 0.008 and the Y axis we have 0.005. And as you can see where we kind of zoomed in on the squiggle now and you can see that Very clearly hit zero at or the slope it looks like it has an inflection point at the origin. So we can confirm our estimate That the slope is approximately zero my observation at the origin.

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.

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 1 / AB Educators

Catherine Ross

Heather Zimmers

Caleb Elmore

Michael Jacobsen

Calculus 1 / AB Courses

Recommended Videos

Watch More Solved Questions in Chapter 2

Video Transcript

James Stewart

Calculus: Early Transcendentals

Catherine Ross

Heather Zimmers

Caleb Elmore

Michael Jacobsen

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

Calculus: Early Transcendentals

Catherine Ross

Heather Zimmers

Caleb Elmore

Michael Jacobsen

James StewartCalculus: Early Transcendentals

Catherine Ross

Heather Zimmers

Caleb Elmore

Michael Jacobsen

James Stewart

Calculus: Early Transcendentals