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

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0try dividing with the highest power

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0\(\large\color{slate}{\displaystyle\lim_{x \rightarrow ~0}~\frac{x^2+3}{x^4}}\) like this?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0Well, you can't really do anything besides splitting it into two limits of x\(^2\)/x\(^4\) and 3/x\(^4\).

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0With this being said you will still end up with the limit diverging into \(\infty\).

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so there is no limit?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0it would be 0 if \(x\rightarrow\infty\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so the limit does not exist

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0\(\large\color{slate}{\displaystyle\lim_{x \rightarrow ~0}~\frac{x^2+3}{x^4}=\lim_{x \rightarrow ~0}~\frac{x^2}{x^4}+\lim_{x \rightarrow ~0}~\frac{3}{x^4}=\lim_{x \rightarrow ~0}\frac{1}{x^2}+3\lim_{x \rightarrow ~0}\frac{1}{x^4}=\infty }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0you 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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