Question

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

Answer 1

/\y
difference quotient = ------- right?
/\x

Answer 2

what is that????

Answer 3

the change in "y"
that is the difference quotient; -------------
the change in "x"

Answer 4

2t
---- is your equation right?
3-t

Answer 5

when we divide everything by"t" we end up with -2....not that I know what thats sposed to help :)

Answer 6

gr8

Answer 7

but you can't divide evrything by t.....that's false maths

Answer 8

yes you can... multiply by 1/t//1/t it equals 1

Answer 9

2t*(1/t) = 2
--------- -------
(3-t)(1/t) = 3/t - t/t

Answer 10

they are equal equations

Answer 11

as t-> infinity; we get 2/-1 = -2

Answer 12

but how that helps out, I dont know :)

Answer 13

perhaps you problem here is that you want to find:

A(t+h) - A(t)
---------- is that right?
h

Answer 14

amistres.....exactly....u are a genius....pliz continue

Answer 15

lol.... im a genius when compared to fish :)

ok; we just fill in our equation with this new jargon...

Answer 16

[2(t+h)/ 3-(t+h)] - [2t/ 3-t] //h ; the "//h" just means all on top of h

Answer 17

2t+2h 2t
------ - ---- //h
3-t+h 3-t

lets get like demoninators and add away

Answer 18

(3-t)(2t+2h) - (3-t-h) 2t
---------------------- //h
(3-t+h)(3-t)

Answer 19

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)

Answer 20

3t +6h -6t
---------- //h
(3-t-h)(3-t)

Answer 21

-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?

Answer 22

i kind of gat lost how does (3-t)(1/t) =1

Answer 23

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

Answer 24

3/t goes to zero; and -t/t = -1

Answer 25

oooh ok didn know that

Answer 26

I gotta recheck something, I think I forgot how to add :)

Answer 27

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)

Answer 28

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)

Answer 29

when h=0; we get 6/(3-t)^2

Answer 30

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 :)

Answer 31

wow thanx alot