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Math Help - Limits

  1. #1
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    Limits

    Deduce that if |x -3| < 1, then |(x + 2)^(2) - 25| < 11|x - 3|

    Use this result to show, without using the Limit Laws, that

    lim x -> 3 of (x + 2)^(2) = 25

    I am really confused and dont understand this question
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  2. #2
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    Quote Originally Posted by SyNtHeSiS View Post
    Deduce that if |x -3| < 1, then |(x + 2)^(2) - 25| < 11|x - 3|

    Use this result to show, without using the Limit Laws, that

    lim x -> 3 of (x + 2)^(2) = 25

    I am really confused and dont understand this question

     |x-3|<1

     |(x+2)^2 - 25| = |(x+2)^2 - 5^2| = |(x+2-5)(x+2+5)|

     = |(x-3)(x+7)|

    Also from |x-3|<1 , we have  2<x<4 so  9 < x+7 < 11

    Therefore ,  |(x+2)^2 - 25| = |x-3||x+7| < 11|x-3|


    For the second part , we have to prove it by checking the definition ... What similarity between part 1 and the definition can you find ?
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  3. #3
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    How are you suppose to know that it is suppose to be manipulated in that way? I would never have thought of that
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