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Math Help - Differential

  1. #16
    is up to his old tricks again! Jhevon's Avatar
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    so dy is an approximation of deltay, they are not always exactly the same
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  2. #17
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Jhevon View Post
    so dy is an approximation of deltay, they are not always exactly the same
    This is true. I was just commenting to my girlfriend that it seems slightly unfair that the question set is talking about approximations (using dy) then asks a question about exact answers (using (Delta)y) but doesn't say it wants exact. Confusing!

    -Dan
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    Re:

    Yes Jhevon you are correct!!! Now I just have to figure out why...I will examine you work and see how you came up with the solution...
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    Quote Originally Posted by qbkr21 View Post
    Yes Jhevon you are correct!!! Now I just have to figure out why...I will examine you work and see how you came up with the solution...
    Given a function f(x) and a points x and x + a (where a is, presumably, small) we define:
    (Delta)f = f(x + a) - f(x)

    -Dan
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  5. #20
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by qbkr21 View Post
    I mean the big LN out in front confuses me I know that:


    (1/2)ln


    but then to I recopy the problem and log the 2nd half this, and this is the point in which I get confused. If the big LN were not there I would

    (1/2)[(6x+5)/(7x-4)^(-1/2) then I would differentiate the inside using the quotient rule for the inside of the square root. I really am stuck Jhevon.
    you could do the quotient rule, but it would be too much work i think, we want to make the problem as easy as possible, calculus is already hard on its own. tell me at what step i lost you and i'll walk you through it
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  6. #21
    is up to his old tricks again! Jhevon's Avatar
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    either i'm zoning out, or this thread is moving really fast, everytime i click submit i see like 3 new post!
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  7. #22
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    Re:

    Give me a moment and will have it worked out...
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  8. #23
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    Re:

    Quote Originally Posted by Jhevon View Post
    see if this solution works:

    y = 5sqrt(x)

    now, (delta)y = f(x + (delta)x) - f(x)

    now f(x + deltax) = f(1 + 0.3) = f(1.3) = 5.700877125

    f(x) = f(1) = 5

    => deltay = 5.700877125 - 5 = 0.700877125
    wait but when you plugged the values into the formula


    f(x + (delta)x) - f(x) I see how you got the 1.3 but how is that equal to
    5.700877125? Did you just stick it back in the original problem Jhevon ?
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  9. #24
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by qbkr21 View Post
    Yes Jhevon you are correct!!! Now I just have to figure out why...I will examine you work and see how you came up with the solution...
    Dan's formula looks neater than mine, so let me use that.

    let delta x = a, then we have

    delta y = f(x + a) - f(x), why? here's an explanation. it would be better with a graph, but let's see if i can do it in words.

    delta y is the change in y that results from a change in x. delta x = a is a small change in x.

    now remember that f(x) gives the y value for any x

    so if the first x coordinate is x and then we have a small change of a, so that the second coordinate is x + a. then the change in y will be given by the difference of the y values between the two. the y value at x is f(x) and the y value at x + a is f(x + a) so the change in y will be the difference between the two y values, namely f(x + a) - f(x)
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  10. #25
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by qbkr21 View Post
    wait but when you plugged the values into the formula


    f(x + (delta)x) - f(x) I see how you got the 1.3 but how is that equal to
    5.700877125? Did you just stick it back in the original problem Jhevon ?

    yes, i pluged 1.3 in the original. see the explanation above
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  11. #26
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    Re:

    I am still a bit confused with the big LN, but I gave it a whirl:

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  12. #27
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by qbkr21 View Post
    I am still a bit confused with the big LN, but I gave it a whirl:

    see the quotient rule makes it complicated. what i did was to use the laws of logarithms to simplify. the laws i used are as follows:

    ln(x)^n = nln(x) ..........this is how we got to take the 1/2 power down in front.

    ln(x/y) = ln(x) - ln(y) ..........i used this to separate the fraction into two managable pieces.
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  13. #28
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    Quote Originally Posted by qbkr21 View Post
    I am still a bit confused with the big LN, but I gave it a whirl:

    by the way, your way of doing it is incomplete. you need to find the derivative of ln[(6x + 5)/(7x - 4)] which is (7x - 4)/(6x + 5) * that quotient rule thing
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  14. #29
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    Re:

    Updated work:

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  15. #30
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by qbkr21 View Post
    Updated work:

    almost correct. you have to distribute the 1/2


    (1/2)ln(x/y) = (1/2)[ln(x) - ln(y)] = (1/2)ln(x) - (1/2)ln(y)
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