Question

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?

Answer 1

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

Answer 2

No @Zale101

Answer 3

How's it like then?

Answer 4

\[\frac{ -6+x }{ x^4 }\]

Answer 5

^ @Zale101

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

Ok thank you!

Answer 11

@Zale101 Could you help me with a couple more?

Answer 12

Sure.