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-   -   (Calculus) Epsilon Delta Proofs (https://www.askmehelpdesk.com/showthread.php?t=227603)

  • Jun 16, 2008, 08:48 PM
    tntitansgirl
    (Calculus) Epsilon Delta Proofs
    Use the Epsilon-Delta definition to prove the limit is L.

    lim (4x+9)=21
    x-> 3
  • Jun 17, 2008, 05:13 AM
    galactus


    We must show that given any positive number , we can find another

    positive number such that satisifies

    ... [1]

    Whenever x satisfies ... [2].

    To find , we can rewrite [1] as

    or

    or ... [/3]

    We must choose so that [3] is satisfied whenever [2]

    is satisfied. So we take .

    Now, can you see that the last step and finish?
  • Jun 17, 2008, 08:50 AM
    tntitansgirl
    Quote:

    Originally Posted by galactus
    Now, can you see that the last step and finish?.

    4(E/4) = E

    Is that the last step? Thanks for your help! You are awesome, galactus!
  • Jun 17, 2008, 10:08 AM
    galactus
    To prove this choice works for , suppose that x satisfies [2].

    Since we are letting , it follows from [2]

    that x satisfies

    Therefore, [3] is satisfied since it is just the right hand inequality in

    This proves that

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