anonymous
  • anonymous
Use the information to evaluate the limits. I have a drawing attached.
Mathematics
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anonymous
  • anonymous
Use the information to evaluate the limits. I have a drawing attached.
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
|dw:1342983331687:dw|
anonymous
  • anonymous
@apoorvk Let me draw out the options from which I have to answer.
anonymous
  • anonymous
|dw:1342983428659:dw|

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anonymous
  • anonymous
we can do one at a time .there are 4. but heres A^
anonymous
  • anonymous
apoorvk
  • apoorvk
That's: lim [4 f(x)] ---> right? x ->c and [.] represents greatest integer function (GIF) - right?
anonymous
  • anonymous
Yes, and I think?
apoorvk
  • 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
  • anonymous
yeah
anonymous
  • anonymous
so would it be lim f(4)?
apoorvk
  • apoorvk
umm no, actually, that's 4 times the limits - \[[4 \times \lim \limits_{x\rightarrow c}^{}f(x) ]\]
anonymous
  • anonymous
Oh okay, how would I solve that?
apoorvk
  • apoorvk
and \(\lim \limits_{x\rightarrow c}^{}f(x) = 3/2\) is already given!
anonymous
  • anonymous
Ok
anonymous
  • anonymous
so what would we do divide 4?
anonymous
  • anonymous
im confsued.. what do we do
anonymous
  • 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
  • anonymous
lol. Ok so for a, we still have [4 lim f(x)] as x approaches c.. ok
apoorvk
  • 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
  • anonymous
Yes, ok
anonymous
  • anonymous
So then a is: 6?
anonymous
  • anonymous
Can I write b now?
apoorvk
  • apoorvk
yes! sure
anonymous
  • anonymous
Kk im drawing now!
anonymous
  • anonymous
|dw:1342985761573:dw|
anonymous
  • anonymous
Is it just 2? I'm not sure
apoorvk
  • apoorvk
hey I need to make one thing sure - is that [.] for a step-up function or just general brackets?
apoorvk
  • apoorvk
if nothing's been stated, they're probably just general brackets~
anonymous
  • anonymous
what do you mean, sorry
anonymous
  • anonymous
Its lim [4f(x)] for a.
apoorvk
  • 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
  • anonymous
So a is still 6? and b is 2? lim [4f(x)] for a is exactly how it written
apoorvk
  • apoorvk
because:|dw:1342986392700:dw|
anonymous
  • anonymous
ok cool! so far i have a as 6, b as 2. Ill write c now
anonymous
  • anonymous
|dw:1342986644322:dw|
apoorvk
  • 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
  • anonymous
ok I wrote c. it says; lim[f(x)g(x)] as x-->c
apoorvk
  • apoorvk
Okay here you use the funda: |dw:1342986659285:dw|
anonymous
  • anonymous
Ok so would c be 3/4?
anonymous
  • anonymous
?
apoorvk
  • apoorvk
yeah right!
anonymous
  • anonymous
yay! ok heres d
anonymous
  • anonymous
|dw:1342987062541:dw|
anonymous
  • anonymous
lim f(x)/g(x) as x--> c = ??
apoorvk
  • apoorvk
okay same way as the others - can you try this? You need to separate the two limits and then divide them.
anonymous
  • anonymous
Ok would it be 3?
anonymous
  • anonymous
|dw:1342987382978:dw|
apoorvk
  • apoorvk
Yeah right! good work!
anonymous
  • anonymous
thanks so much
apoorvk
  • apoorvk
no worries :]

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