A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
Given the lim(3x7)=2 as x>3. Using the epsilondelta definition for the given epsilon=.01 find the corresponding delta > 0 such that (3x7)  2 < .01 whenever x3 < delta
anonymous
 one year ago
Given the lim(3x7)=2 as x>3. Using the epsilondelta definition for the given epsilon=.01 find the corresponding delta > 0 such that (3x7)  2 < .01 whenever x3 < delta

This Question is Closed

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3So when \(\large\rm \epsilon=0.01\), there exists a \(\large\rm \delta\gt0\) such that\[\large\rm 0\ltx3\lt\delta\qquad\implies\qquad (3x7)2\lt0.01\] So start with your epsilon equation, trying to find an x3 in there.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3\[\large\rm 3x9\lt0.01\]Do you see it? :) It's so close!!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0sorry I suck at math lol

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3Well you're not trying to solve for x in this inequality! :O careful!\[\large\rm \color{orangered}{x3}\lt\delta\]You're trying to make this orange part show up in your epsilon equation.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3So if I factor out a 3,\[\large\rm 3(\color{orangered}{x3})\lt0.01\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3And divide the 3 over to the other side,\[\large\rm \color{orangered}{x3}\lt\frac{1}{300}\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3If you compare these two inequalities:\[\large\rm \color{orangered}{x3}\lt\delta\qquad\qquad\qquad \color{orangered}{x3}\lt\frac{1}{300}\]It looks like we've found our delta, do you see it? :o

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3I rewrote 0.01 as 1/100 and then divided by 3, or multiplied by 1/3, just in case that middle step was confusing.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3cee peeeeeee +_+ where you at broski? brain esplode?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thanks so much, i understand it a little better now

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3ya these are super weird :U calc gets a lot more fun once you get past this initial stuff

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0can you help me with one more?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thanks!given the epsilondelta definition prove that lim(3x5)=7 as x > 4

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so would it become x4 < \[\epsilon \div 3\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so delta would be epsilon/3

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3Mmm ya that sounds right! :) If they say "prove" then maybe we need to write it up formally, with some words and stuff...

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3\[\large\rm \lim_{x\to4}3x5=7\] Let \(\large\rm \epsilon\gt0\). There exists a \(\large\rm \delta\gt0\) such that \[\large\rm \text{if}\quad 0\ltx4\lt\delta\qquad\text{then}\qquad f(x)7\lt\epsilon\] \[\large\rm f(x)7\lt\epsilon \quad\text{if and only if}\quad 3x57\lt\epsilon\]\[\large\rm \text{if and only if}\quad3x12\lt\epsilon\]\[\large\rm \text{if and only if}\quadx4\lt\frac{\epsilon}{3}\] Choose \(\large\rm \delta=\dfrac{\epsilon}{3}\). Thus, \(\large\rm 0\ltx4\lt\dfrac{\epsilon}{3}\) and it follows that \(\large\rm f(x)7\lt\epsilon\). Maybe something like that? :p Bah I can't remember how to write these properly.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3But ya you've got the right idea with finding the corresponding delta value :D

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3The first type of problem is a little easier to deal with, you're just looking for a specific number. In the second problem you're generalizing for every epsilon, so you gotta be careful :O

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Nothing to add, you've done a fine job @zepdrix :)

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3What do you think cee pee? :o Too much with the words? It's just each step following the previous step. Relating delta to the epsilon/3 is really the important part though, which it seems like you've figured out.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.