schmidtdancer
Use the information to evaluate the limits. I have a drawing attached.
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schmidtdancer
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|dw:1342983331687:dw|
schmidtdancer
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@apoorvk Let me draw out the options from which I have to answer.
schmidtdancer
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|dw:1342983428659:dw|
schmidtdancer
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we can do one at a time .there are 4. but heres A^
schmidtdancer
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@apoorvk ?
apoorvk
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That's: lim [4 f(x)] ---> right?
x ->c
and [.] represents greatest integer function (GIF) - right?
schmidtdancer
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Yes, and I think?
apoorvk
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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?
schmidtdancer
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yeah
schmidtdancer
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so would it be lim f(4)?
apoorvk
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umm no, actually, that's 4 times the limits -
\[[4 \times \lim \limits_{x\rightarrow c}^{}f(x) ]\]
schmidtdancer
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Oh okay, how would I solve that?
apoorvk
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and \(\lim \limits_{x\rightarrow c}^{}f(x) = 3/2\) is already given!
schmidtdancer
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Ok
schmidtdancer
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so what would we do divide 4?
schmidtdancer
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im confsued.. what do we do
schmidtdancer
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@apoorvk
apoorvk
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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:
\[[ 4.\lim\limits_{x \rightarrow c}f(x)]\]
schmidtdancer
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lol. Ok so for a, we still have [4 lim f(x)] as x approaches c.. ok
apoorvk
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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:
\[4 \times (3/2)\]
schmidtdancer
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Yes, ok
schmidtdancer
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So then a is: 6?
schmidtdancer
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Can I write b now?
apoorvk
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yes! sure
schmidtdancer
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Kk im drawing now!
schmidtdancer
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|dw:1342985761573:dw|
schmidtdancer
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Is it just 2? I'm not sure
apoorvk
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hey I need to make one thing sure - is that [.] for a step-up function or just general brackets?
apoorvk
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if nothing's been stated, they're probably just general brackets~
schmidtdancer
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what do you mean, sorry
schmidtdancer
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Its lim [4f(x)] for a.
apoorvk
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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!
schmidtdancer
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So a is still 6? and b is 2? lim [4f(x)] for a is exactly how it written
apoorvk
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because:|dw:1342986392700:dw|
schmidtdancer
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ok cool! so far i have a as 6, b as 2. Ill write c now
schmidtdancer
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|dw:1342986644322:dw|
apoorvk
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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.
schmidtdancer
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ok I wrote c. it says; lim[f(x)g(x)] as x-->c
apoorvk
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Okay here you use the funda:
|dw:1342986659285:dw|
schmidtdancer
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Ok so would c be 3/4?
schmidtdancer
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?
apoorvk
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yeah right!
schmidtdancer
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yay! ok heres d
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|dw:1342987062541:dw|
schmidtdancer
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lim f(x)/g(x) as x--> c = ??
apoorvk
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okay same way as the others - can you try this? You need to separate the two limits and then divide them.
schmidtdancer
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Ok would it be 3?
schmidtdancer
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|dw:1342987382978:dw|
apoorvk
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Yeah right! good work!
schmidtdancer
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thanks so much
apoorvk
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no worries :]