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Math Help - Limits part 1?

  1. #1
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    Limits part 1?

    Can anyone help me with these two limit without using l hospital rule which I do not know.

    1. As x approaches zero

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

    2. As x approaches -2

    (x^3+8)/(x^2-4) This is what I did

    x(x^2+8)/(x+2)(x-2) Can anyone help me continue.
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    Re: Limits part 1?

    Quote Originally Posted by homeylova223 View Post
    Can anyone help me with these two limit without using l hospital rule which I do not know.

    1. As x approaches zero

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

    \displaystyle \lim_{x\to 0} \frac{(x+2)^2-4}{x} or \displaystyle \lim_{x\to 0} (x+2)^2-\frac{4}{x} ?
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    Re: Limits part 1?

    Quote Originally Posted by homeylova223 View Post


    x(x^2+8)/(x+2)(x-2) Can anyone help me continue.
    \displaystyle x^3+8 \neq x(x^2+8) , do you know why?

    Consider \displaystyle a^3+b^3 = (a+b)(a^2-ab+b^2)
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    Re: Limits part 1?

    Yes I see but how would I proceed?
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    Re: Limits part 1?

    Quote Originally Posted by homeylova223 View Post
    Yes I see but how would I proceed?
    factor x^3+8 correctly, then cancel the common factor in the numerator and denominator ... finally, sub in x = -2
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