find xy+(z^3)x-2yz=0 in terms of z

- anonymous

find xy+(z^3)x-2yz=0 in terms of z

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- anonymous

whts in terms of z mean?

- anonymous

the answer should be z= f(x,y). so i am asking what f(x,y) is

- amistre64

x.z^3 -2yz = -xy

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## More answers

- amistre64

z(-2y +x.z^2) = -xy
-2y +x.z^2 - -xy/z

- anonymous

It's complicated to solve for z.

- anonymous

yeah its a cubic eqn in z

- anonymous

Could you write the original question, if it is not this?

- amistre64

-2y +x.z^2 = -xy/z
x.z^2 = (-xy+2yz)/z
z^3 = (-xy+2yz)/x

- anonymous

i am supposed to find dz/dx at the point (1,1,1) of that equation

- anonymous

then say that

- anonymous

spo i assumed i needed z as a function of x and y

- amistre64

you dont need to solve for z then...

- anonymous

u dont need to..i think not

- amistre64

dz/dx = g(F).d(xbar)/dx

- anonymous

ok, sorry about tha

- anonymous

You don't have to solve for z.

- anonymous

bt then how to do it???

- amistre64

get the gradient vector but partialling the equation of the plane there

- amistre64

get the gradient vector but partialling the equation of the plane there

- anonymous

then do df/dx / df/dz?

- amistre64

- amistre64

plug in the values from your point know to get the gradianet vector

- amistre64

<2,-1,1> is your normal vector/gradient..

- anonymous

oh ok, i got the gradient vector, then plug in the point (1,1,1) to df/dx to get the answer?

- amistre64

dot product that with the vecotr that is the point...<1,1,1>

- anonymous

i got <2, -1, 1> yes

- amistre64

2(x-1)-1(y-1)+1(z-1) = dz/dx i think :)

- anonymous

is it right??

- anonymous

is that the plane equation?

- anonymous

i dont have the answer

- amistre64

that is the plane equation

- anonymous

doesnt the gradient vector give ... in that case we can simply do df/dx / df/dz???

- anonymous

the answer isnt an equation...its a value

- amistre64

him; dunno havent read that far yet :)

- anonymous

thats wht m sayin

- anonymous

is the answer 2???

- amistre64

the answer would be 2 then right?

- amistre64

gradient . point

- anonymous

i think so! thanks!

- anonymous

is it 2??

- anonymous

i dont know the value, but it seems right

- anonymous

u understood how it ws done?

- amistre64

i dont think I evenknow how it was done lol

- anonymous

I got -2.

- anonymous

yes, get the gradient, and plug in the x,y and z valuse of the point into the gradient and divide df/dx by df/dz to get dz/dx right?

- anonymous

Not entirely sure though.

- anonymous

i thnk it shld be right..there might b calculation errors bt b surev f d method

- amistre64

<2,-1,1>
<1, 1,1>
---------
2 -1 +1 = 2

- anonymous

so i said

- anonymous

david wht grade u in?

- anonymous

im a sophomore in college. im studying for my calc 3 final

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