Question

Find the limit of the function algebraically.

limit as x->0 of
-6+x/x^4

Answer 1

@satellite73

Answer 2

@iGreen

Answer 3

I'm not completely sure what this is asking for you to do.

Answer 4

To find the limit,

Answer 5

But i dont think its with direct substitution

Answer 6

@Jim766

Answer 7

@wio

Answer 8

Post it correctly, using parentheses, so we can tell what it is. Or post a screenshot

Answer 9

Attempts?

Answer 10

well I tried plugging in 0 for x, but oviously thats not going to work, :C

Answer 11

So then i tried to expand the denominator

Answer 12

Which still leaves 3 x's on the bottom

Answer 13

@Hero

Answer 14

@Luigi0210

Answer 15

@hartnn

Answer 16

can you use L'Hopital's Rule ?

Answer 17

I am not familiar with that

Answer 18

ok, then factor out 'x' from the numerator, can you ?

Answer 19

I've hear of the Power rule, but i'm in precalculus and apparently they dont show you that

Answer 20

yes we have -3/x^3

Answer 21

i mean -6/x^3

Answer 22

how??

i was talking about this :
\(\Large -6+x= x [\dfrac{-6}{x}+1]\)

got this ?

Answer 23

hm? How did you get that?

Answer 24

nvm, then forget it..

Answer 25

simply plug in x=0 in numerator and denominator, what do u get ?

Answer 26

negative 6,

Answer 27

and in denominator ?

Answer 28

0 right,

Answer 29

its -6+0/0^4

Answer 30

yes, correct
\(\Large \dfrac{-6}{0} = -\infty \)

do you get why it is NEGATIVE infinity ?

Answer 31

because the 6 is negative and the (asymptote) is going farther down negative y values?

Answer 32

wait does that mean the limit doesnt exist?

Answer 33

\(-\infty \) is the limiting value of your function.
it is still a value.
Limit will not exist ONLY IF , right hand limit does NOT equal to left hand limit.

Answer 34

I would say the limit does not exist. It diverges to \(-\infty\)

Answer 35

Ohhh, okay, thank you @hartnn and @Zarkon

Answer 36

but left hand limit = right hand limit {= \(-\infty \)}so limit should exist.
and
welcome ^_^

Answer 37

Ahh okay!! C:

Answer 38

a limit converges if there is a number L such that the left and right hand limits give the same value L (L is some real number)

infinity is not a real number

Answer 39

I mean my answer choices are 6, 0, -6, and does not exist

Answer 40

@Zarkon

Answer 41

then you should surely choose DNE.

Answer 42

oh okay, thank you C: