Limit question?

- AmTran_Bus

Limit question?

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- AmTran_Bus

|dw:1436286205012:dw|

- AmTran_Bus

Um. Here are my choices but Im getting DNE

##### 1 Attachment

- AmTran_Bus

Just had an idea

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## More answers

- AmTran_Bus

What in the world someone help!http://www.wolframalpha.com/input/?i=limit+as+x+approaches+0+%28e%5Ex-6%29%2Fsin+4x

- AmTran_Bus

The problem does not say from the left or right!!!!!!!!! So my DNE is right but what do I do?

- SolomonZelman

\(\large\color{slate}{\displaystyle\lim_{x \rightarrow ~0}\frac{e^x-6}{\sin(4x)}}\) ?

- AmTran_Bus

Correct

- welshfella

would l'hopitals rule be helpful here?

- AmTran_Bus

Good thought. Let me try it

- SolomonZelman

can't do it yet

- SolomonZelman

it is not 0/0 when you plug in x=0

- welshfella

right - only the denoiminator = 0
l'hopitals no help

- AmTran_Bus

Oh yea, must be inf/inf or 0/0

- welshfella

as x approaches 0 sin 4x approaches 0
and e^x - 6 approaches -5
so can we then say that the limit is - infinity?

- welshfella

- approaching from above 0

- SolomonZelman

you are right, the limit actually doesn't exst.

- AmTran_Bus

Yea, thats what has thrown me off for a long time. But wolfram treats it as 0+ and 0- and and the answer choices have both neg inf and pos inf

- SolomonZelman

even one sides limits diverge

- SolomonZelman

when you get a limit that is equal to +∞ or -∞, that means the limit does NOT exist. (It is infinite - not limited)

- AmTran_Bus

But it is an ans choice!

- SolomonZelman

Well, for two sides limit, it DNE

- AmTran_Bus

I agree

- SolomonZelman

from the right side it is ∞, from the left side it is -∞

- AmTran_Bus

dumb problem and ans choices

- SolomonZelman

do you have an answer choice does not exist?

- AmTran_Bus

##### 1 Attachment

- welshfella

yes near the y axis the graph looks like
|dw:1436287092439:dw|

- AmTran_Bus

@SolomonZelman

- AmTran_Bus

@welshfella so do you agree DNE?

- welshfella

yes

- AmTran_Bus

Well thanks for all your help! I may email prof

- AmTran_Bus

Well, I asked on yahoo ans and they said -inf. I just dont see it but gotta mark something @hartnn @SolomonZelman @welshfella

- hartnn

limit shouldn't exist
sin 4x is negative when x<0
and it is positive when x>0
hence Left hand limit would not = right hand limit

- AmTran_Bus

I agree hartnn. Just these ans choices giving fit.

- SolomonZelman

ok, maybe the question is a little bit different?

- AmTran_Bus

??

- SolomonZelman

Are you sure it is exactly saying
\(\Large\color{slate}{\displaystyle\lim_{x \rightarrow ~0}\frac{e^x-6}{\sin(4x)}}\)

- SolomonZelman

well, then this limit doesn't exist.

- SolomonZelman

I mean if limit=∞ or -∞ it doesn't exist (either way)

- hartnn

people saying -infinity are assuming that sin4x = 0
e^x -6 will be negative

- SolomonZelman

ohh...

- SolomonZelman

yeah, should have noticed that:)

- SolomonZelman

Bus?

- AmTran_Bus

I'm here! So is it -inf after all?

- SolomonZelman

yes

- AmTran_Bus

Sin 4x=0?

- SolomonZelman

yes

- hartnn

no lol,
the limit is still DNE.
In yahoo answer, they might have said -inf as they might have assumed sin4x =0 ...
that was my point,
but sin 4x is not actually 0

- SolomonZelman

well, if you take the limit of sin(4x) as x→0 alone, then it is 0

- AmTran_Bus

Story of my life...

- hartnn

why would you do that lol...

- SolomonZelman

1 D, XD = (1+x)D

- SolomonZelman

jk

- SolomonZelman

idk, hartnn

- AmTran_Bus

Gonna email prof

- SolomonZelman

the limit is indeterminate, beause you are trying to divide by zero

- SolomonZelman

technically u r...

- SolomonZelman

when you divide by a number that approaches 0 from the right, you get ∞,
and when you divide by a number that approaches 0 from the left, you get -∞.
if the divident is positive.
In this case divident is negative, so it is the other way around.
when you divide by a number that approaches 0 from the right, you get -∞,
and when you divide by a number that approaches 0 from the left, you get ∞.
And if you take a 2-sides limit (as in your case), you shouldn't get just ∞ or -∞.....

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