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Math Help - limit to negative infinity

  1. #1
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    limit to negative infinity

    Use a table of values of f(x) to estimate the value of the limit to four decimal places.

    idk if I am just not knowing how to do this, but if someone could walk me through this I would be more than greatful!
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  2. #2
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    Quote Originally Posted by ryan18 View Post
    Use a table of values of f(x) to estimate the value of the limit to four decimal places.

    idk if I am just not knowing how to do this, but if someone could walk me through this I would be more than greatful!
    what about using the "trick" that i showed you in the other post?
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  3. #3
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    Quote Originally Posted by felper View Post
    what about using the "trick" that i showed you in the other post?
    What do you mean? Multiplying it by the same thing just a + instead of a -? Sorry I am horrible with LaTeX I tried, but it didnt turn out right.
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  4. #4
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    Yeah. See that link http://www.wolframalpha.com/input/?i=limit+x+to+-infinity+(sqrt(3x^2%2B4x%2B5)-sqrt(3x^2%2B3x%2B7)) and try the "technique" that i told you.
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  5. #5
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    \lim_{x\rightarrow-\infty} \sqrt{3x^2+4x+5}-\sqrt{3x^2+3x+7}

    \lim_{x\rightarrow-\infty} \sqrt{3x^2+4x+5}-\sqrt{3x^2+3x+7}\frac{(\sqrt{3x^2+4x+5}+\sqrt{3x^2  +3x+7})}{(\sqrt{3x^2+4x+5}-\sqrt{3x^2+3x+7})}

    \lim_{x\rightarrow-\infty}\frac{3x^2+4x+5-(3x^2+3x+7)}{\sqrt{3x^2+4x+5}+\sqrt{3x^2+3x+7}}

    \lim_{x\rightarrow-\infty}\frac{x-2}{\sqrt{3x^2+4x+5}+\sqrt{3x^2+3x+7}}

    \lim_{x\rightarrow-\infty}\frac{-(x-2)/|x|}{(\sqrt{3x^2+4x+5}+\sqrt{3x^2+3x+7})/|x|}

    \lim_{x\rightarrow-\infty}\frac{-(1-\frac{2}{x})}{\sqrt{3+\frac{4}{x}+\frac{5}{x^2}}+\  sqrt{3+\frac{3}{x}+\frac{7}{x^2}}}

    \lim_{x\rightarrow-\infty}\frac{-(1-0)}{\sqrt{3+0+0}+\sqrt{3+0+0}}

    \lim_{x\rightarrow-\infty}\frac{-1}{\sqrt{3}+\sqrt{3}}=\frac{-1}{2\sqrt{3}}

    Holy mother I can't believe I typed that all out.
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  6. #6
    dMh
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    There was a solution already posted similar to this question here:

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  7. #7
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    Wouldn't it be better to do what the problem told you to do?

    The problem said "Use a table of values of f(x) to estimate the limit to four decimal places".

    When x= -1000, that expression is -0.2894.
    When x= -1000000 that expression is -0.2887.

    etc.
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