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Math Help - Evaluate the limit

  1. #1
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    Evaluate the limit

    Evaluate the limit :

    lim (e^2x- 2x -1 )/ x^2
    x-> 0

    Somebody can help me ?
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  2. #2
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    Quote Originally Posted by VinhT View Post
    Evaluate the limit :

    lim (e^2x- 2x -1 )/ x^2
    x-> 0

    Somebody can help me ?
    L'Hopital ... twice.
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  3. #3
    Super Member Random Variable's Avatar
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     \lim_{x \to 0} \frac{e^{2x}-2x-1}{x^{2}} = \lim_{x \to 0} \frac{(1+2x+\frac{(2x)^2}{2!}+\frac{(2x)^{3}}{3!}+  ...)-2x-1}{x^{2}}

     = \lim_{x \to 0} \frac{\frac{(2x)^2}{2!}+\frac{(2x)^{3}}{3!}+...}{x  ^{2}} = \lim_{x \to 0} \Big(2 + \frac{4x}{3} + ...\Big) = 2
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  4. #4
    Super Member Random Variable's Avatar
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