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Posted by on Saturday, February 25, 2012 at 11:58am.

Evaluate the limit:
lim 25-(x+2)^2 / x-3
x->3

  • Calculus - , Saturday, February 25, 2012 at 12:15pm

    25(x-3) = 25 x -75

    so
    [ 25 x -75 - x^2 - 4 x - 4 ] /(x-3)

    [-x^2 + 21 x -79 ] / (x-3)

    (x-3) is not a factor of the numerator so I can not get rid of it in the denominator.
    as x goes to 3 the numerator becomes -25 and the denominato is 0 so undefined is the answer.
    If you mistyped it and mean
    [ 25-(x+2)^2 ]/ (x-3 )
    then
    [ 25 - x^2 - 4 x - 4 ]/ (x-3)
    that is
    [ - x^2 - 4 x + 21 ] / (x-3)
    - [ x^2 + 4 x - 21 ] / (x-3)
    - (x-3)(x+7) / (x-3)
    -x - 7
    -3 - 7
    -10
    PLEASE US PARENTHESES SO WE CAN TELL NUMERATOR FROM DENOMINATOR !!!!!

  • Calculus - , Saturday, February 25, 2012 at 12:19pm

    sorry! the question was
    lim [25 - (x+2)^2] / [x-3]
    x->3

  • Calculus - , Saturday, February 25, 2012 at 12:22pm

    so
    -10

  • Calculus - , Saturday, February 25, 2012 at 12:23pm

    I figured you must have mistyped it because (x-3) simply had to be a factor of the numerator or the question would not have been asked.

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