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anonymous

  • 4 years ago

find the limit please \[\lim_{x \rightarrow infinity}\sqrt{x^2+3x+1}-x\]

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  1. myininaya
    • 4 years ago
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    you should put a 1 underneath that and rationalize the numerator by multiplying top and bottom by the conjugate of the top

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

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

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

  5. myininaya
    • 4 years ago
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    |x|=x if x>0 which it is since x gets positive large

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

  7. myininaya
    • 4 years ago
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    \[\frac{3+0}{\sqrt{1+0+0}+1}\]

  8. anonymous
    • 4 years ago
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    thanks once again

  9. myininaya
    • 4 years ago
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    lol np

  10. anonymous
    • 4 years ago
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    this is the last one, can you help me with it please

  11. anonymous
    • 4 years ago
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    Compute A= x^2+x/x+1 as x approaches +infinity and B= x^2+x/x^2+1 as x approaches -infinity

  12. anonymous
    • 4 years ago
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    \[\lim_{x \rightarrow +\infty} (x^2+x) / (x+1) = +\infty\]\[\lim_{x \rightarrow -\infty}(x^2 +x)/(x^2+1) =1\]

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