Question

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

Answer 1

try dividing with the highest power

Answer 2

what do you mean?

Answer 3

\(\large\color{slate}{\displaystyle\lim_{x \rightarrow ~0}~\frac{x^2+3}{x^4}}\) like this?

Answer 4

yes

Answer 5

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

Answer 6

With this being said you will still end up with the limit diverging into \(\infty\).

Answer 7

so there is no limit?

Answer 8

or is the limit 0?

Answer 9

it would be 0 if \(x\rightarrow\infty\)

Answer 10

so the limit does not exist

Answer 11

\(\large\color{slate}{\displaystyle\lim_{x \rightarrow ~0}~\frac{x^2+3}{x^4}=\lim_{x \rightarrow ~0}~\frac{x^2}{x^4}+\lim_{x \rightarrow ~0}~\frac{3}{x^4}=\lim_{x \rightarrow ~0}\frac{1}{x^2}+3\lim_{x \rightarrow ~0}\frac{1}{x^4}=\infty }\)

Answer 12

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 ∞