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Math Help - Evaluate Limits help

  1. #1
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    Thumbs down Evaluate Limits help

    I give up on these three How do you evaluate these using limit properties :*( Help?


    (1) lim x-->0 sin 3x / x + x^2 + x^3



    (2)lim x-->3 sqrt x^2 + 7 − sqrt x + 13 / sqrt x^3 − 2 − sqrt 2x + 19 (each sqrt covers the entire poly)



    (3)lim x-->+infiniti 2x^2 + |x| cosx/ 3x^2 + 5
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  2. #2
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    <br />
\lim_{x \rightarrow\ 0} \frac{sin(3x) + x^3 + x^4}{x}<br />

    If you plugh in 0 for x, you get 0/0.

    Use L'Hopital's rule.
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  3. #3
    Super Member General's Avatar
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    Quote Originally Posted by alexsmith2139 View Post
    I give up on these three How do you evaluate these using limit properties :*( Help?


    (1) lim x-->0 sin 3x / x + x^2 + x^3



    (2)lim x-->3 sqrt x^2 + 7 − sqrt x + 13 / sqrt x^3 − 2 − sqrt 2x + 19 (each sqrt covers the entire poly)



    (3)lim x-->+infiniti 2x^2 + |x| cosx/ 3x^2 + 5
    Specify them.
    The first one is \frac{sin(3x)}{x+x^2+x^3} or \frac{sin(3x)}{x}+x^2+x^3 ??!
    Use brackets to make them readable.
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  4. #4
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    ^Yes, General is right. The first one I "assumed" that it was (sin(3x))/x without any other denominators.
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