lilfayfay
Consider the curve defied by the equation y+cosy = x +1 for 0< or to equal y < or to equal 2pi
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lilfayfay
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@Goten77
Goten77
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hmm
Umangiasd
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Okay, i considered it, now what?
lilfayfay
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a.) Find dy/dx in terms of y.
b.) Write an equation for each vertical tangent to the curve
c.) Find d^2y/dx^2 in terms of y.
lilfayfay
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wouldn't be like this? |dw:1358131334593:dw|
lilfayfay
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sorry about my bad handwriting my hands are cold :P
Goten77
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no it wont be like that cause you with with respect to Y
lilfayfay
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ok so part a.) is just 1-siny=x'
dumbcow
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they are looking for dy/dx or y'
derivative wrt x BUT in terms of y
Goten77
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oh derp.... i did it wrong
lilfayfay
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lol
lilfayfay
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so was my technique correct? :D
Goten77
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|dw:1358139066897:dw|
Goten77
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k so y did it not show both images.... the 1st part wwas expanded 2nd part is simplified
lilfayfay
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wait how did u get that?
Goten77
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|dw:1358139147928:dw|
Goten77
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this program some times deletes my images or it doesnt appear for whatever reason
lilfayfay
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o.o
Goten77
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|dw:1358139329704:dw|
Goten77
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get it now?
lilfayfay
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how does x cancel from the other side?
Goten77
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|dw:1358139425312:dw|
Goten77
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when/where did i cancel a x?
lilfayfay
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from the right original side of equation (x+1)
lilfayfay
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oh ok i think i see why u canceled the variables on the right side of the equation :)
lilfayfay
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so 1/(1-siny) is part a.)?
Goten77
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the x didnt cancel
the derivative of x+1 = just 1 since its wrt x
Goten77
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and yes thats your part a
lilfayfay
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ok how do i do part b.)
Goten77
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hmm
Goten77
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so vertical asymptotes is what makes the bottom of a fraction = 0
Goten77
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|dw:1358140100389:dw|
Goten77
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but we need the vertical asymptote so we needa find the x value so we put the equation in the form of x = #
Goten77
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so now we use the original equation and use that y value to solve for the x
lilfayfay
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how did u get 1=siny
Goten77
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|dw:1358140410824:dw|
Goten77
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so the vertical graph is
x= (pi - 2)/ 2
Goten77
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i got 1=siny because it was 1st
1-siny= 0
i just moved it over
Goten77
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|dw:1358140649853:dw| sorry im bad at spelling
Goten77
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ok so part c is finding the 2nd derivative.... this will be fun
Goten77
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|dw:1358140714426:dw|
lilfayfay
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so part b.) is (pi -2)/2
Goten77
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|dw:1358140838951:dw|
Goten77
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|dw:1358140982676:dw|
Goten77
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this is basically the quotient rule + implicint differentation + production rule + chain rule THEN use that negative .... you dont have to simplify unless ur told to.. which i dont think u can
lilfayfay
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so cosy/(1-siny)^2 is the answer? :)
Goten77
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yee
lilfayfay
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k, ty ^^
lilfayfay
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can you help me with 1 more pls? :)
Goten77
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sure