Question

Find the limit of the function algebraically.

Answer 1

@Jhannybean

Answer 2

Does not exist?
-6 + x/x^4
-6+0/0 =
-6/0 = undefined?

Answer 3

or expand -6 + x / (x^3)(x),
cancel out the x's to
-6/x^3
still -6/0

Answer 4

\[\bf \lim_{x \rightarrow 0}\frac{ -6+x }{ x^4 }=\lim_{x \rightarrow 0}\frac{ -6 }{ x^4 }+\frac{ 1 }{ x^3 }=-6\infty+\infty=-\infty\]If you observe, the -6/x^4 approaches negative infty and 1/x^3 has a limit of positive infinity. But -6/x^4 approaches negative infinity much faster since the denominator gets larger faster hence it becomes a smaller value faster than 1/x^3 becomes a larger value. When we add the results, they tend to the negative side and eventually approach negative infinity.

Answer 5

Confusing lol :S

Answer 6

It could also be translated like this:\[\bf =-6 \infty+\infty =-5\infty = -\infty\]

Answer 7

negative infinity isnt one of my options this time :l
6

0

-6

Does not exist

Answer 8

I've simply extended the realms of mathematics so that one can do arithmetic with infinitely large values but still get to the right answer.

Answer 9

so it would be -6 instead of does not exist right?

Answer 10

no.

Answer 11

it's negative infinity, like I've stated already.

Answer 12

well because it's not one of my options, I have to select does not exist?

Answer 13

Think of it like this:\[\bf -6\infty = -\infty\]No matter what I multiply a value that is becoming infinity small by, it's still going to remain and approach and infinitely small value. Hence -6*negative infinity simply translates in to being a negative small value.

Answer 14

It wouldn't exist because the function is shooting out to infinity so fast that the numerator has nothing it an do but follow it to infinity as well.

Answer 15

Compare the powers of x^4 and x.

lets say x = 2.

which is greater? (2)^4 or 2?

Answer 16

ahhhh okay! does that apply to any number in the same situation? for instance: 9+x/x^3 if x->0 again?

Answer 17

Yes,infinity is just a really large number.

Answer 18

One can also think of it like this: By substituting 0 for x we get:\[\bf \lim_{x \rightarrow 0}\frac{ -6+x }{ x^4 }=\frac{ -6 }{ 0 }=-6 \times \frac{1}{0}=-6 \times \infty=-\infty\]

Answer 19

Exactly like that :)

Answer 20

This is confusing but i think im starting to get it.

Answer 21

Try graphing and understanding the behavior of the function. Infinity is just a number placeholder. It helps you determine the behavior of the function as x approaches a really large number.

Answer 22

The limit is `approaching` negative infinity.
It can't ever `equal` that value.

Maybe that's why your option is "does not exist".

Answer 23

I get it now! thanks