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Math Help - Limit Questions

  1. #1
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    Limit Questions

    Any help would be wonderful, please work out the answers too, I'm just learning!


    lim
    x→ 2

    x^2−4x+4 / x^2+x−6



    lim
    x→ 0

    x / |x|





    lim
    x→ 1

    x^3−1 / x−1





    lim
    x→ 1

    x^2+4x−5 / x^2+x−2





    lim
    x→ 2

    x^3−8 / 12(x−2)
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  2. #2
    Junior Member
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    Quote Originally Posted by youmuggles View Post
    Any help would be wonderful, please work out the answers too, I'm just learning!


    lim
    x→ 2

    x^2−4x+4 / x^2+x−6

    i'll start you off

    (x-2)(x-2)/(x+3)(x-2)= (x-2)/(x+3)

    lim
    x→ 2
    (x-2)/(x+3) =0
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  3. #3
    Super Member General's Avatar
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    Quote Originally Posted by youmuggles View Post
    Any help would be wonderful, please work out the answers too, I'm just learning!


    lim
    x→ 2

    x^2−4x+4 / x^2+x−6




    lim
    x→ 0

    x / |x|





    lim
    x→ 1

    x^3−1 / x−1





    lim
    x→ 1

    x^2+4x−5 / x^2+x−2





    lim
    x→ 2

    x^3−8 / 12(x−2)
    For the first one:
    \frac{x^2-4x+4}{x^2+x-6}=\frac{(x-2)(x-2)}{(x+3)(x-2)}
    The bad guys cancel, and you will find your limit by direct substitution.
    Similary for the rest expect the second one.

    For the second one, you should consider the limit as x goes to zero from right and from left.
    and remember that:
    If \lim_{x \to a^{+}} f(x) \neq \lim_{x \to a^{-}} f(x)
    then  \lim_{x \to a} f(x) does not exist.
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  4. #4
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    When I do these questions, these are my answers... Could someone please tell me what i am doing wrong..?

    Quote Originally Posted by youmuggles View Post
    Any help would be wonderful, please work out the answers too, I'm just learning!


    lim
    x→ 2

    x^2−4x+4 / x^2+x−6

    (x-2)(x-2)
    (x-2)(x+3)

    (x-2)
    (x+3)

    ((2)-2)
    ((2+3)

    0
    5

    = 0


    Quote Originally Posted by youmuggles View Post
    lim
    x→ 0

    x / |x|
    x
    x

    = 0? DNE?

    I still don't fully understand the concept with this one..



    Quote Originally Posted by youmuggles View Post
    lim
    x→ 1

    x^3−1 / x−1
    (x-1)(x^2+2x+1)
    (x-1)

    x^2-2x+1

    (1)^2 - 2(1) + 1

    1-2+1

    = 0



    Quote Originally Posted by youmuggles View Post
    lim
    x→ 1

    x^2+4x−5 / x^2+x−2
    (x+5)(x-1)
    (x-1)(x-1)

    (x+5)
    (x-1)

    ((1)+5)
    ((1)-1)

    6
    0

    = DNE



    Quote Originally Posted by youmuggles View Post
    lim
    x→ 2

    x^3−8 / 12(x−2)

    (x-2)(x^2+4x+4)

    12(x-2)

    (x^2+4x+4)
    12

    ((2)^2 + 4(2) + 4
    12

    4+8+4
    12

    =4/3
    Last edited by youmuggles; January 17th 2010 at 02:44 PM. Reason: wrote answer wrong.
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  5. #5
    Super Member General's Avatar
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    Kuwait
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    Quote Originally Posted by youmuggles View Post
    When I do these questions, these are my answers... Could someone please tell me what i am doing wrong..?




    (x-2)(x-2)
    (x-2)(x+3)

    (x-2)
    (x+3)

    ((2)-2)
    ((2+3)

    0
    5

    = 0

    correct

    x
    x

    = 0? DNE?

    I still don't fully understand the concept with this one..

    if x \rightarrow 0^{+}, then |x|=x
    if x \rightarrow 0^{-}, then |x|=-x



    (x-1)(x^2+2x+1)
    (x-1)
    Wrong, This is the formula a^3-b^3=(a-b)(a^2+ab+b^2)
    Try to do it again.
    x^2-2x+1

    (1)^2 - 2(1) + 1

    1-2+1

    = 0





    (x+5)(x-1)
    (x-1)(x-1)
    No No No, Try to factor the denominator again.
    (x+5)
    (x-1)

    ((1)+5)
    ((1)-1)

    6
    0

    = DNE





    (x-2)(x^2+4x+4)
    Same mistake, The formula is a^3-b^3=(a-b)(a^2+ab+b^2)
    Try to do it again.
    12(x-2)

    (x^2+4x+4)
    12

    ((2)^2 + 4(2) + 4
    12

    4+8+4
    12

    =4/3
    .................
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  6. #6
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    Posts
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    (x-2)(x^2+2x+4)
    12(x-2)

    (x^2+2x+4)
    12

    ((2)^2 + 2(2) + 4
    12

    4+4+4
    12

    =1
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  7. #7
    Super Member General's Avatar
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    Kuwait
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    Quote Originally Posted by youmuggles View Post
    (x-2)(x^2+2x+4)
    12(x-2)

    (x^2+2x+4)
    12

    ((2)^2 + 2(2) + 4
    12

    4+4+4
    12

    =1
    Mwahahaha !
    Yes ! You got it !
    You > Calculus
    You are correct.
    Try to use LaTeX to write your math equations.
    No need for this complicated way.
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