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anonymous

  • 4 years ago

find the limit of this please \[\lim_{x \rightarrow -infinity}(5x+12)/\sqrt{9x^2+x-3}\]

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  1. myininaya
    • 4 years ago
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    \[\lim_{x \rightarrow -\infty}\frac{5x+12}{\sqrt{9x^2+x-3}} \cdot \frac{\frac{1}{\sqrt{x^2}}}{\frac{1}{\sqrt{x^2}}}\] now recall \[\sqrt{x^2}=|x|=x \text{ if } x<0 \] x<0 since we are approaching negative infinity so we have \[\lim_{x \rightarrow -\infty}\frac{5x+12}{\sqrt{9x^2+x-3}} \cdot \frac{\frac{1}{-x}}{ \frac{1}{\sqrt{x^2}}}\]

  2. myininaya
    • 4 years ago
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    \[\lim_{x \rightarrow -\infty} \frac{-5+\frac{-12}{x}}{\sqrt{9+\frac{1}{x}-\frac{3}{x^2}}}\]

  3. myininaya
    • 4 years ago
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    \[\frac{-5 +0}{\sqrt{9+0-0}}\]

  4. myininaya
    • 4 years ago
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    oops small type-0 |x|=-x if x<0

  5. myininaya
    • 4 years ago
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    everything else is good

  6. anonymous
    • 4 years ago
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    is the final answer -5/sqrt 9

  7. myininaya
    • 4 years ago
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    the sqrt(9)=3

  8. anonymous
    • 4 years ago
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    ok i see thanks again myininaya

  9. myininaya
    • 4 years ago
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    np

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