anonymous
  • anonymous
find the limit of the function algebraically. x^2+3/x^4 x=0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
try dividing with the highest power
anonymous
  • anonymous
what do you mean?
SolomonZelman
  • SolomonZelman
\(\large\color{slate}{\displaystyle\lim_{x \rightarrow ~0}~\frac{x^2+3}{x^4}}\) like this?

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anonymous
  • anonymous
yes
SolomonZelman
  • SolomonZelman
Well, you can't really do anything besides splitting it into two limits of x\(^2\)/x\(^4\) and 3/x\(^4\).
SolomonZelman
  • SolomonZelman
With this being said you will still end up with the limit diverging into \(\infty\).
anonymous
  • anonymous
so there is no limit?
anonymous
  • anonymous
or is the limit 0?
SolomonZelman
  • SolomonZelman
it would be 0 if \(x\rightarrow\infty\)
anonymous
  • anonymous
so the limit does not exist
SolomonZelman
  • SolomonZelman
\(\large\color{slate}{\displaystyle\lim_{x \rightarrow ~0}~\frac{x^2+3}{x^4}=\lim_{x \rightarrow ~0}~\frac{x^2}{x^4}+\lim_{x \rightarrow ~0}~\frac{3}{x^4}=\lim_{x \rightarrow ~0}\frac{1}{x^2}+3\lim_{x \rightarrow ~0}\frac{1}{x^4}=\infty }\)
SolomonZelman
  • SolomonZelman
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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