A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 3 years ago
Let \[f(x) = x^2  2x +1 \] use the epsilondelta definition to show that: \[\lim_{x \rightarrow 3} f(x) = 4\]
I've come up with this:
\[( x1)^2  4 < \epsilon \]
\[ x3 < \sqrt{\epsilon } \]
Set delta as the squareroot of epsilon:
\[ x3 < \delta =\sqrt{\epsilon } \]
How do I finish this, I get it all wrong by taking the left expresson to the second power
anonymous
 3 years ago
Let \[f(x) = x^2  2x +1 \] use the epsilondelta definition to show that: \[\lim_{x \rightarrow 3} f(x) = 4\] I've come up with this: \[( x1)^2  4 < \epsilon \] \[ x3 < \sqrt{\epsilon } \] Set delta as the squareroot of epsilon: \[ x3 < \delta =\sqrt{\epsilon } \] How do I finish this, I get it all wrong by taking the left expresson to the second power

This Question is Closed

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1How do you have the limit is 4? You won't be able to prove what you said. That does x>2 right? So f>2^22(2)+1=44+1=0+1=1

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Well, that the limit is 4 was given in the assignment and \[f(x)=x2−2x+=4 \]. where x=3 I think you got the limit wrong it's \[ x \rightarrow 3\]

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1Ok. I couldn't read that little number.

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1Thanks. So you have x^22x+14<E x^22x3<E (x3)(x+1)<E (x3)(x+1)<E x3<E/x+1 I would choose d<1 And then choose the number in the interval of x that gives me the smallest E/x+1

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1E is epsilon d is delta by the way :)

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1I hope that helps. I will try to check back with you later. I have to go for now, but I return in like 2 hours :(

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Got it! Thanks a lot, really appreciate it! :D

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1Great remember when showing that limit above you have to say let d=min{1, E/x+1 where you have chosen x based off letting d<1}

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1Oh and wow. I can read that 3 on this computer but not that other one.
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.