Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

frx Group Title

Let \[f(x) = x^2 - 2x +1 \] use the epsilon-delta definition to show that: \[\lim_{x \rightarrow 3} f(x) = 4\] I've come up with this: \[|( x-1)^2 - 4| < \epsilon \] \[| x-3| < \sqrt{\epsilon } \] Set delta as the squareroot of epsilon: \[| x-3| < \delta =\sqrt{\epsilon } \] How do I finish this, I get it all wrong by taking the left expresson to the second power

  • one year ago
  • one year ago

  • This Question is Closed
  1. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    How do you have the limit is 4? You won't be able to prove what you said. That does x->2 right? So f->2^2-2(2)+1=4-4+1=0+1=1

    • one year ago
  2. frx Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Well, 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 \[ x \rightarrow 3\]

    • one year ago
  3. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Ok. I couldn't read that little number.

    • one year ago
  4. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Thanks. So you have |x^2-2x+1-4|<E |x^2-2x-3|<E |(x-3)(x+1)|<E |(x-3)||(x+1)|<E |x-3|<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|

    • one year ago
  5. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    E is epsilon d is delta by the way :)

    • one year ago
  6. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I 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 :(

    • one year ago
  7. frx Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Got it! Thanks a lot, really appreciate it! :D

    • one year ago
  8. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Great 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}

    • one year ago
  9. myininaya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Oh and wow. I can read that 3 on this computer but not that other one.

    • one year ago
    • Attachments:

See more questions >>>

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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.