compute the difference quotient of the given function; A(t)=2t/ 3-t

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compute the difference quotient of the given function; A(t)=2t/ 3-t

Mathematics
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/\y difference quotient = ------- right? /\x
what is that????
the change in "y" that is the difference quotient; ------------- the change in "x"

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2t ---- is your equation right? 3-t
when we divide everything by"t" we end up with -2....not that I know what thats sposed to help :)
gr8
but you can't divide evrything by t.....that's false maths
yes you can... multiply by 1/t//1/t it equals 1
2t*(1/t) = 2 --------- ------- (3-t)(1/t) = 3/t - t/t
they are equal equations
as t-> infinity; we get 2/-1 = -2
but how that helps out, I dont know :)
perhaps you problem here is that you want to find: A(t+h) - A(t) ---------- is that right? h
amistres.....exactly....u are a genius....pliz continue
lol.... im a genius when compared to fish :) ok; we just fill in our equation with this new jargon...
[2(t+h)/ 3-(t+h)] - [2t/ 3-t] //h ; the "//h" just means all on top of h
2t+2h 2t ------ - ---- //h 3-t+h 3-t lets get like demoninators and add away
(3-t)(2t+2h) - (3-t-h) 2t ---------------------- //h (3-t+h)(3-t)
gotta adjust for my own stupidity here... (3-t-h) is what it should have been... 3t +6h -2t^2 -2th - [6t -2t^2 -2th] ------------------------------ //h (3-t-h)(3-t)
3t +6h -6t ---------- //h (3-t-h)(3-t)
-3t +6h ---------- //h multiply top and bottom by 1/h (3-t-h)(3-t) -3t +6h ------------- (3-t-h)(3-t)(h) we good so far?
i kind of gat lost how does (3-t)(1/t) =1
when we get a variable stuck on the bottom, then the limit goes to 0 as that variable gets really big: for example; 1 --------------------- = .000000000...000000001 10000000...00000000 which is very very tiny
3/t goes to zero; and -t/t = -1
oooh ok didn know that
I gotta recheck something, I think I forgot how to add :)
right here....... 6t +6h -2t^2 -2th - [6t -2t^2 -2th] ------------------------------ //h (3-t-h)(3-t) 6h ---------- //h ; thats better, told ya I forgot how to add :) (3-t-h)(3-t)
6h ---------- //h ; now we multiply (1/h) top and bottom (3-t-h)(3-t) 6h ------------- //(h/h) (3-t-h)(3-t)(h) ---------------------- 6 ------------- thats our answer (3-t-h)(3-t)
when h=0; we get 6/(3-t)^2
A = 2t/ 3-t A' = (3-t)(2) - (2t)(-1)//(3-t)^2 A' = 6-2t +2t // (3-t)^2 A' = 6/(3-t)^2 ....see much quicker :)
wow thanx alot

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