Use the information to evaluate the limits. I have a drawing attached.

- anonymous

Use the information to evaluate the limits. I have a drawing attached.

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- anonymous

|dw:1342983331687:dw|

- anonymous

@apoorvk Let me draw out the options from which I have to answer.

- anonymous

|dw:1342983428659:dw|

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## More answers

- anonymous

we can do one at a time .there are 4. but heres A^

- anonymous

@apoorvk ?

- apoorvk

That's: lim [4 f(x)] ---> right?
x ->c
and [.] represents greatest integer function (GIF) - right?

- anonymous

Yes, and I think?

- apoorvk

Ohkay... so.. that basically means I guess:
|dw:1342983884987:dw|
You have the value of that limit inside provided, you need to plug it in and proceed - understandable?

- anonymous

yeah

- anonymous

so would it be lim f(4)?

- apoorvk

umm no, actually, that's 4 times the limits -
\[[4 \times \lim \limits_{x\rightarrow c}^{}f(x) ]\]

- anonymous

Oh okay, how would I solve that?

- apoorvk

and \(\lim \limits_{x\rightarrow c}^{}f(x) = 3/2\) is already given!

- anonymous

Ok

- anonymous

so what would we do divide 4?

- anonymous

im confsued.. what do we do

- anonymous

@apoorvk

- apoorvk

Cool down your nerves - nothing to get confused about! :) (ain;t no monster :P lol)
I just brought the whole limit expression inside the GIF brackets - we can do that since it will not affect the limit value).
Then, since \(\large \lim\limits_{x \rightarrow t}k.f(x) = k.\lim\limits_{x \rightarrow t}f(x)\), for any function f(x) and constant k, I take the '4' out of the limit, and I end up with:
\[[ 4.\lim\limits_{x \rightarrow c}f(x)]\]

- anonymous

lol. Ok so for a, we still have [4 lim f(x)] as x approaches c.. ok

- apoorvk

Now it's given (in your first whiteboard drawing above) that \(\lim \limits_{x\rightarrow c}f(x) = 3/2\), I substitute that value into \([4\lim \limits_{x\rightarrow c}f(x)]\), an hence now I get:
\[4 \times (3/2)\]

- anonymous

Yes, ok

- anonymous

So then a is: 6?

- anonymous

Can I write b now?

- apoorvk

yes! sure

- anonymous

Kk im drawing now!

- anonymous

|dw:1342985761573:dw|

- anonymous

Is it just 2? I'm not sure

- apoorvk

hey I need to make one thing sure - is that [.] for a step-up function or just general brackets?

- apoorvk

if nothing's been stated, they're probably just general brackets~

- anonymous

what do you mean, sorry

- anonymous

Its lim [4f(x)] for a.

- apoorvk

has anything been stated for those square brackets? If not am guessing they are just normal parenthesis, and not for GIF - in that case the second one would be 2 alright!

- anonymous

So a is still 6? and b is 2? lim [4f(x)] for a is exactly how it written

- apoorvk

because:|dw:1342986392700:dw|

- anonymous

ok cool! so far i have a as 6, b as 2. Ill write c now

- anonymous

|dw:1342986644322:dw|

- apoorvk

See, if [.] represents GIF, it should be mentioned, because in my education system, the rule is generally they would mention it if it is for a GIF - I am not sure about how's it stated in Us schools.

- anonymous

ok I wrote c. it says; lim[f(x)g(x)] as x-->c

- apoorvk

Okay here you use the funda:
|dw:1342986659285:dw|

- anonymous

Ok so would c be 3/4?

- anonymous

?

- apoorvk

yeah right!

- anonymous

yay! ok heres d

- anonymous

|dw:1342987062541:dw|

- anonymous

lim f(x)/g(x) as x--> c = ??

- apoorvk

okay same way as the others - can you try this? You need to separate the two limits and then divide them.

- anonymous

Ok would it be 3?

- anonymous

|dw:1342987382978:dw|

- apoorvk

Yeah right! good work!

- anonymous

thanks so much

- apoorvk

no worries :]

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