help with limits please.... medals

- Anikate

help with limits please.... medals

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- jamiebookeater

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- Anikate

cool. imma post a pic real quick

- Anikate

##### 1 Attachment

- Anikate

g and l

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## More answers

- jtvatsim

g should be similar to the very first question. I'm going to predict that this is some sort of infinity.

- jtvatsim

It's hard for me to see i) so I'll hold my predictions.... :)

- Anikate

I got undefined after plugging in thr x value

- jtvatsim

OK, so if that's good enough for your teacher, then you are done. Otherwise you can try an x a little to the left and/or right as needed.

- jtvatsim

Or graph it! :)

- Anikate

|dw:1433996948686:dw|

- Anikate

thats the question

- jtvatsim

So there is a little - sign below the limit?

- Anikate

yea

- jtvatsim

So you could try an x slightly to the left of 4 if you like.

- Anikate

ok 3.9?

- jtvatsim

Sure that should do it. A graph will also reveal which infinity this is.

- Anikate

I got -20 after plugging in 3.9

- Anikate

I want t

- Anikate

try

- Anikate

i want to try and do these without graphing, cuz were not supposed ot

- Anikate

to*

- jtvatsim

Well, in that case... :)

- jtvatsim

Best answer at this point then since you got a negative, would be to say this is negative infinity.

- Anikate

got it

- Anikate

and can you show me how to do l

- Anikate

its the second to last one

- jtvatsim

|dw:1433997229274:dw|

- jtvatsim

Sure thing, let's see it!

- jtvatsim

I can make out everything except the x information under the limit.

- Anikate

|dw:1433997257410:dw|

- Anikate

thats the questions

- jtvatsim

cool

- Anikate

yup

- jtvatsim

Alright, so we obviously will get a 0 on the bottom, but let's look at the top, what is cos(0)?

- Anikate

why 0 on the bottom?

- Anikate

i thoght x turn to 1 in hospitals

- jtvatsim

Only if you get 0/0 as the limit when you first plug in. It's a key restriction.

- jtvatsim

L'Hospital only works when the limit is 0/0 exactly.

- jtvatsim

In this case, we actually get 1/0. Since cos(0) = 1.

- Anikate

oh ok

- jtvatsim

Tricky fish!

- Anikate

right lol

- Anikate

so what do we do from here?

- jtvatsim

So this is yet another infinity it seems. :)

- Anikate

isnt 1/0 undefined?

- jtvatsim

That's true. But just like we were doing before, when you get undefined, it might be positive or negative infinity.

- Anikate

oh ok, and how would u find?

- jtvatsim

Plug in x a little to the left. AND also an x a little to the right. We have to do both in this case because there isn't a left or right hand limit.

- Anikate

ok

- jtvatsim

It's a two sided limit (no + or - subscript thing).

- jtvatsim

Nevermind, that would be ridiculous.

- Anikate

wait, but the x is = 0

- Anikate

lollolol

- jtvatsim

yes, yes, I'm falling asleep here. :)

- Anikate

lol its 1am here, same

- jtvatsim

Anyways, maybe I should let you make the suggestions... zzzz

- Anikate

-1 and 1?

- jtvatsim

OK, you might want to get a little tighter than that, I'd say -0.1 and 0.1 just to be safe.

- Anikate

ok

- jtvatsim

You don't want the equation to think you are testing for x = 1 and x = -1... it has feelings too. :)

- Anikate

i got -9.9 and 9.9

- Anikate

lol

- jtvatsim

Well, isn't that interesting? From the left, it looks like negative infinity. But from the right it looks like positive infinity.

- jtvatsim

The left-hand limit does not equal the right-hand limit, this limit Does Not Exist!

- Anikate

ya, this cray cray

- Anikate

oh cool

- Anikate

got it thanks!

- jtvatsim

What's weird is that it isn't even Undefinied. It literally does not even exist! :)

- jtvatsim

Awesome. Glad to help! Good luck with your studies! :)

- Anikate

oh whats the difference?

- jtvatsim

Undefined usually means it's some sort of infinity. It's just not a "normal" number.

- Anikate

ooooh ok

- jtvatsim

In this case, the right hand limit flies up to positive infinity, while the left hand limit flies down to negative infinity, leaving a huge break in the gap going in opposite directions.

- jtvatsim

So, the (two-sided) limit does not exist.

- Anikate

oh sounds good! thanks for all ur help! get

- Anikate

time to get some sleep haha!
good night!

- jtvatsim

Your welcome! Ah... yes... sleep.... zzzz -.-

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