Problem

A machinist is required to manufacture a circular…

View

Problem 10 Medium Difficulty

Given that $ \displaystyle \lim_{x \to \pi}\csc^2 x = \infty $, illustrate Definition 6 by finding values of $ \delta $ that correspond to (a) $ M = 500 $ and (b) $ M = 1000 $.

Name: given that displaystyle lim_x to picsc2 x infty illustrate definition 6 by finding values of delta t
Uploaded: 2017-10-03
Duration: 6 min 18 s
Channel: Numerade
Description: Given that $ \displaystyle \lim_{x \to \pi}\csc^2 x = \infty $, illustrate Definition 6 by finding values of $ \delta $ that correspond to (a) $ M = 500 $ and (b) $ M = 1000 $.

Answer

(a) $\delta=0.04473$
(b) $\delta=0.03163$

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 2

Limits and Derivatives

Section 4

The Precise Definition of a Limit

Discussion

You must be signed in to discuss.

C L.

August 26, 2021

fuck you stupid ass website making me pay. I want to get my work done .

Andrew R.

September 16, 2021

Dont waste your money didnt even help show how to do it

Top Calculus 1 / AB Educators

Grace H.

Anna Marie V.

Campbell University

Heather Z.

Oregon State University

Kristen K.

University of Michigan - Ann Arbor

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

Video Transcript

This is problem number ten of this tour Calculus eighth edition, section two point four. Given that the limit as X approaches pi, of course he can. Squared X is equal to Community Hill Astri definition six by finding values of Delta that corresponded to a M equals five hundred and B m equals one thousand. So for a reference, we're going to write definition six, which were given limits and sex and purchase A of a function he called to infinity here. All right. Zero is less than the quantity X minus a absolutely of the quantity west in the delta. And then the function is greater than I am some value and and to help us with this ah, problem. I have provided a a sketch of the co sign Sorry, cause he can score it function, which is our FX in this case. And we see that the coast seeking squared function and is this shape where every multiple pie beginning at zero zero pie to pie or zero negative pining to buy There is no defined a portion of the graph and we see that the ah there is an infinite limited each of these asam toots so high The limit definitely approaches positive. Infinity as X approaches pine. But we're trying to listrik definition six using these. No, these terms here Then we have discussed that we're going to find Delta values in order. Teo ones that are related to Emma's five hundred m is one thousand. So what we do is we use a graphene tool. We take this function cause he connects and we throw a Corsican Sorry, Costigan squared X. We put this in any graphing calculator in any graphing tool and we're going to do is we're going to try to find it a value for don't tell that satisfies this condition. So let's take the first part party Emma's five hundred. So there will be a point here much, much higher than one. But such that fine y equals one hundred. Well, across this ako seek support function. And if we take this here, for example, this point where across is because he can square function, Erm we can estimate on and use a trace function using using a tracing tool on a graphing calculator to determine exactly where this point lines. And if we do that, we should see that this ah, is it is at approximately three point, the X values approximately three point zero nine seven came. And what deserves to show us is that the difference between three point zero nine seven and pine is this distance here between the function at a height of five hundred, the function and the Assam tote, or eh X equals a and this defined there were daughter because we know that for the function being greater than M in party Emma's five hundred So among the function is greater than him. As you can see in this region pi plus this delta Hi minus two Stilton rate symmetric about X equals pine and the way we determine no time or one is this difference This Ah, this small difference between fine and exactly that we found at the height of nine hundred five hundred and we see that this is approximately point zero four. So that is our first told. Other corresponds with this height of five hundred essentially for any delta equal to or less than point zero four. In the end, he arranged there, we're guarantee that the function is greater than the value five hundred. If we further increase our scope of the function to an M equals one thousand for partying. We see that we reach our A next value. That is approximately three point one one. So notice that we've got even closer to pie, which guarantee that our doctor is going to be even smaller, not much smaller but smaller. And we see that we're gonna approximate value of point zero three. So this makes sound sensitive. We increased our restriction on the function f co sequence cortex that it must be greater than a thousand. We must confirmed Delta that is smaller because it is in this region, this higher region. So essentially within point zero three core les from pine, the function is restricted to this don't mean to this range of f greater than a thousand for part B. So we've found our two Delta bis that correspond to party and party on this. These are our final answers

Daniel J.

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 2

Limits and Derivatives

Section 4

The Precise Definition of a Limit

Problem

A machinist is required to manufacture a circular…

Problem 10 Medium Difficulty

Given that $ \displaystyle \lim_{x \to \pi}\csc^2 x = \infty $, illustrate Definition 6 by finding values of $ \delta $ that correspond to (a) $ M = 500 $ and (b) $ M = 1000 $.

Answer

(a) $\delta=0.04473$
(b) $\delta=0.03163$

Related Courses

Calculus: Early Transcendentals

Related Topics

Discussion

Top Calculus 1 / AB Educators

Grace H.

Anna Marie V.

Heather Z.

Kristen K.

Calculus 1 / AB Courses

Precalculus Review - Intro

Functions on the Real Line - Overview

Recommended Videos

Watch More Solved Questions in Chapter 2

Video Transcript

Calculus: Early Transcendentals

Grace H.

Anna Marie V.

Heather Z.

Kristen K.

Precalculus Review - Intro

Functions on the Real Line - Overview

(a) $\delta=0.04473$(b) $\delta=0.03163$

Calculus: Early Transcendentals

Grace H.

Anna Marie V.

Heather Z.

Kristen K.

Precalculus Review - Intro

Functions on the Real Line - Overview

Grace H.

Anna Marie V.

Heather Z.

Kristen K.

(a) $\delta=0.04473$
(b) $\delta=0.03163$