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Math Help - Finding Limits

  1. #1
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    Finding Limits

    I need to find the lim (squ(1+2x)-squ(1+3x)) / (x+2x^2) as x goes to 0 and where x>0.

    Would you multiply by the conjugate?
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    Quote Originally Posted by frenchguy87 View Post
    I need to find the lim (squ(1+2x)-squ(1+3x)) / (x+2x^2) as x goes to 0 and where x>0.

    Would you multiply by the conjugate?
    Do you mean the limit of:


     \frac{(1+2x)^2-(1+3x)^2}{x+2x^2} as x goes to zero??
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  3. #3
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    Quote Originally Posted by frenchguy87 View Post
    I need to find the lim (squ(1+2x)-squ(1+3x)) / (x+2x^2) as x goes to 0 and where x>0.

    Would you multiply by the conjugate?
    \lim_{x \to 0} \frac{\sqrt{1 + 2x} - \sqrt{1 + 3x}}{x + 2x^2} = \lim_{x \to 0} \frac{(\sqrt{1 + 2x} - \sqrt{1 + 3x})}{(x + 2x^2)} \cdot \frac{ (\sqrt{1 + 2x} + \sqrt{1 + 3x}) }{(\sqrt{1 + 2x} + \sqrt{1 + 3x}) }

    = \lim_{x \to 0} \frac{-x}{(x + 2x^2) (\sqrt{1 + 2x} + \sqrt{1 + 3x}) } = ....
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