Question

m

Answer 1

Is it: \[\lim_{x \rightarrow 0}\frac{ -6+x }{ x^4 }\]

Answer 2

?

Answer 3

yes!

Answer 4

well, if x = 0, you have -6+0 on the top

on the bottom you have what?

Answer 5

0^4?

Answer 6

Doing it algebraically:
First I apply the product rule:\[\lim_{x \rightarrow 0}\frac{ x-6 }{ x^4 }=\lim_{x \rightarrow 0}\frac{ 1 }{ x^4 }*\lim_{x \rightarrow 0}(x-6)\]
Now we solve the limits by substituting 0 for x in the expression:
\[\lim_{x \rightarrow 0}(x-6)=0-6=-6\]
So you have:\[-6*\lim_{x \rightarrow 0}\frac{ 1 }{ x^4 }\]
And we know, as x approaches 0, \[\lim_{x \rightarrow 0}\frac{ 1 }{ x^4 }\] becomes arbitrarily large. So we get: \[-6*infinity=-infinity\]

Answer 7

That isnt one of my answer choices though

Answer 8

What are your choices?

Answer 9

6
0
-6
Does not exist

Answer 10

\[\lim_{x \rightarrow 0}\frac{ -6+x }{ x^4 } = \lim_{x \rightarrow 0}\frac{ -6 }{ x^4 } + \frac{ 1 }{ x^3 }\]

does not exist , DNE, means what :p

http://www.wolframalpha.com/input/?i=-6%2F%280.001%29%5E4+%2B+1%2F%280.001%29%5E3

Answer 11

Yea -infinity, means there isnt a limit.

Answer 12

Oh thank-you :)

Answer 13

In order for their to be a limit, it would need to be convergent.

Answer 14

Oh okay

Answer 15

i am really not sure that advice is all that helpful

from **both** sides of x = 0, the thing goes to \(-\infty\), and that's important

i think your software is offering you DNE as an alternative to any mention of infinity.

i'll ask someone who actually knows something about maths:
@freckles

Answer 16

infinity isn't a number
so you could say the limit does not exist