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

1. anonymous

try dividing with the highest power

2. anonymous

what do you mean?

3. SolomonZelman

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

4. anonymous

yes

5. SolomonZelman

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

6. SolomonZelman

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

7. anonymous

so there is no limit?

8. anonymous

or is the limit 0?

9. SolomonZelman

it would be 0 if $$x\rightarrow\infty$$

10. anonymous

so the limit does not exist

11. SolomonZelman

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

12. 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 ∞