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cool. imma post a pic real quick
g and l
g should be similar to the very first question. I'm going to predict that this is some sort of infinity.
It's hard for me to see i) so I'll hold my predictions.... :)
I got undefined after plugging in thr x value
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.
Or graph it! :)
thats the question
So there is a little - sign below the limit?
So you could try an x slightly to the left of 4 if you like.
Sure that should do it. A graph will also reveal which infinity this is.
I got -20 after plugging in 3.9
I want t
i want to try and do these without graphing, cuz were not supposed ot
Well, in that case... :)
Best answer at this point then since you got a negative, would be to say this is negative infinity.
and can you show me how to do l
its the second to last one
Sure thing, let's see it!
I can make out everything except the x information under the limit.
thats the questions
Alright, so we obviously will get a 0 on the bottom, but let's look at the top, what is cos(0)?
why 0 on the bottom?
i thoght x turn to 1 in hospitals
Only if you get 0/0 as the limit when you first plug in. It's a key restriction.
L'Hospital only works when the limit is 0/0 exactly.
In this case, we actually get 1/0. Since cos(0) = 1.
so what do we do from here?
So this is yet another infinity it seems. :)
isnt 1/0 undefined?
That's true. But just like we were doing before, when you get undefined, it might be positive or negative infinity.
oh ok, and how would u find?
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.
It's a two sided limit (no + or - subscript thing).
Nevermind, that would be ridiculous.
wait, but the x is = 0
yes, yes, I'm falling asleep here. :)
lol its 1am here, same
Anyways, maybe I should let you make the suggestions... zzzz
-1 and 1?
OK, you might want to get a little tighter than that, I'd say -0.1 and 0.1 just to be safe.
You don't want the equation to think you are testing for x = 1 and x = -1... it has feelings too. :)
i got -9.9 and 9.9
Well, isn't that interesting? From the left, it looks like negative infinity. But from the right it looks like positive infinity.
The left-hand limit does not equal the right-hand limit, this limit Does Not Exist!
ya, this cray cray
got it thanks!
What's weird is that it isn't even Undefinied. It literally does not even exist! :)
Awesome. Glad to help! Good luck with your studies! :)
oh whats the difference?
Undefined usually means it's some sort of infinity. It's just not a "normal" number.
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.
So, the (two-sided) limit does not exist.
oh sounds good! thanks for all ur help! get
time to get some sleep haha! good night!
Your welcome! Ah... yes... sleep.... zzzz -.-