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anonymous

  • 5 years ago

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

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  1. amistre64
    • 5 years ago
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    /\y difference quotient = ------- right? /\x

  2. anonymous
    • 5 years ago
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    what is that????

  3. amistre64
    • 5 years ago
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    the change in "y" that is the difference quotient; ------------- the change in "x"

  4. amistre64
    • 5 years ago
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    2t ---- is your equation right? 3-t

  5. amistre64
    • 5 years ago
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    when we divide everything by"t" we end up with -2....not that I know what thats sposed to help :)

  6. anonymous
    • 5 years ago
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    gr8

  7. anonymous
    • 5 years ago
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    but you can't divide evrything by t.....that's false maths

  8. amistre64
    • 5 years ago
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    yes you can... multiply by 1/t//1/t it equals 1

  9. amistre64
    • 5 years ago
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    2t*(1/t) = 2 --------- ------- (3-t)(1/t) = 3/t - t/t

  10. amistre64
    • 5 years ago
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    they are equal equations

  11. amistre64
    • 5 years ago
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    as t-> infinity; we get 2/-1 = -2

  12. amistre64
    • 5 years ago
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    but how that helps out, I dont know :)

  13. amistre64
    • 5 years ago
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    perhaps you problem here is that you want to find: A(t+h) - A(t) ---------- is that right? h

  14. anonymous
    • 5 years ago
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    amistres.....exactly....u are a genius....pliz continue

  15. amistre64
    • 5 years ago
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    lol.... im a genius when compared to fish :) ok; we just fill in our equation with this new jargon...

  16. amistre64
    • 5 years ago
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    [2(t+h)/ 3-(t+h)] - [2t/ 3-t] //h ; the "//h" just means all on top of h

  17. amistre64
    • 5 years ago
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    2t+2h 2t ------ - ---- //h 3-t+h 3-t lets get like demoninators and add away

  18. amistre64
    • 5 years ago
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    (3-t)(2t+2h) - (3-t-h) 2t ---------------------- //h (3-t+h)(3-t)

  19. amistre64
    • 5 years ago
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    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)

  20. amistre64
    • 5 years ago
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    3t +6h -6t ---------- //h (3-t-h)(3-t)

  21. amistre64
    • 5 years ago
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    -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?

  22. anonymous
    • 5 years ago
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    i kind of gat lost how does (3-t)(1/t) =1

  23. amistre64
    • 5 years ago
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    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

  24. amistre64
    • 5 years ago
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    3/t goes to zero; and -t/t = -1

  25. anonymous
    • 5 years ago
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    oooh ok didn know that

  26. amistre64
    • 5 years ago
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    I gotta recheck something, I think I forgot how to add :)

  27. amistre64
    • 5 years ago
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    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)

  28. amistre64
    • 5 years ago
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    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)

  29. amistre64
    • 5 years ago
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    when h=0; we get 6/(3-t)^2

  30. amistre64
    • 5 years ago
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    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 :)

  31. anonymous
    • 5 years ago
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    wow thanx alot

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