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anonymous

  • one year ago

find the limit of the function algebraically. x^2+3/x^4 x=0

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  1. anonymous
    • one year ago
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    try dividing with the highest power

  2. anonymous
    • one year ago
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    what do you mean?

  3. SolomonZelman
    • one year ago
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    \(\large\color{slate}{\displaystyle\lim_{x \rightarrow ~0}~\frac{x^2+3}{x^4}}\) like this?

  4. anonymous
    • one year ago
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    yes

  5. SolomonZelman
    • one year ago
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    Well, you can't really do anything besides splitting it into two limits of x\(^2\)/x\(^4\) and 3/x\(^4\).

  6. SolomonZelman
    • one year ago
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    With this being said you will still end up with the limit diverging into \(\infty\).

  7. anonymous
    • one year ago
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    so there is no limit?

  8. anonymous
    • one year ago
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    or is the limit 0?

  9. SolomonZelman
    • one year ago
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    it would be 0 if \(x\rightarrow\infty\)

  10. anonymous
    • one year ago
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    so the limit does not exist

  11. SolomonZelman
    • one year ago
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    \(\large\color{slate}{\displaystyle\lim_{x \rightarrow ~0}~\frac{x^2+3}{x^4}=\lim_{x \rightarrow ~0}~\frac{x^2}{x^4}+\lim_{x \rightarrow ~0}~\frac{3}{x^4}=\lim_{x \rightarrow ~0}\frac{1}{x^2}+3\lim_{x \rightarrow ~0}\frac{1}{x^4}=\infty }\)

  12. SolomonZelman
    • one year ago
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    you have even powers of x in the denominator (so the result won't be ever negative). And for small ± decimals (the smaller the absolute value of the decimal, the more) the limit will go into ∞

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