## anonymous one year ago limit as x approaches zero of quantity negative six plus x divided by x to the fourth power. Would the limit be 0 or does not exist?

1. Zale101

$\lim_{x \rightarrow 0}~[-6+\frac{x}{x^4}]$ Like this?

2. anonymous

No @Zale101

3. Zale101

How's it like then?

4. anonymous

$\frac{ -6+x }{ x^4 }$

5. anonymous

^ @Zale101

6. Zale101

Oh i see $\lim_{x \rightarrow 0} ~[\large \frac{-6+x}{x^4}]= \\lim_{x \rightarrow 0} ~[\large \frac{\frac{-6}{x^4}+\frac{x}{x^4}}{\frac{x^4}{x^4}}]= \lim_{x \rightarrow 0} ~[\large \frac{\frac{-6}{x^4}+\frac{1}{x^4}}{{1}}]=$

7. Zale101

Now, what happens if i sub in x=0?

8. anonymous

It's 0/1 which is undefined? @Zale101

9. Zale101

$\lim_{x \rightarrow 0} ~[\large \frac{\frac{-6}{x^4}+\frac{1}{x^3}}{1}]=\large \frac{\frac{-6}{0}+\frac{1}{0}}{1}$ Therefore, it does not exist because something over a zero is indeterminate.

10. anonymous

Ok thank you!

11. anonymous

@Zale101 Could you help me with a couple more?

12. Zale101

Sure.