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Math Help - Finding the limit

  1. #1
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    Finding the limit

    I've got these two problems.
    Any help would be appreciated!
    Thanks!
    Attached Thumbnails Attached Thumbnails Finding the limit-m1.jpg   Finding the limit-m2.jpg  
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by BACONATOR View Post
    I've got these two problems.
    Any help would be appreciated!
    Thanks!
    \lim_{x \to \infty}x^2e^{-4x} = \frac{x^2}{e^{4x}}

    using L'hospitals rule twice we get

    \lim_{x \to \infty}\frac{2x}{4e^{4x}}=\lim_{x \to \infty}\frac{2}{16e^{4x}}=\frac{2}{\infty}=0
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  3. #3
    Behold, the power of SARDINES!
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    f(x)=\begin{cases}<br />
\frac{x^2+x-12}{x-3}=\frac{(x+4)(x-3)}{(x-3)}=(x+4) \mbox{ if } x < 3 \\<br />
ae^{x-3} \mbox{ if } x \ge 3<br />
\end{cases}

    so to be cont at x=3 we need

    (3+4)=ae^{3-3} \iff 7=a

    for part b use the limit defintion.
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