Question

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

Answer 1

whts in terms of z mean?

Answer 2

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

Answer 3

x.z^3 -2yz = -xy

Answer 4

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

-2y +x.z^2 - -xy/z

Answer 5

It's complicated to solve for z.

Answer 6

yeah its a cubic eqn in z

Answer 7

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

Answer 8

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

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

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

Answer 9

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

Answer 10

then say that

Answer 11

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

Answer 12

you dont need to solve for z then...

Answer 13

u dont need to..i think not

Answer 14

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

Answer 15

ok, sorry about tha

Answer 16

You don't have to solve for z.

Answer 17

bt then how to do it???

Answer 18

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

Answer 19

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

Answer 20

F=<a,b,c>

a = dz/dx...but not that dz/dx...the funny looking one lol

Answer 21

then do df/dx / df/dz?

Answer 22

<y+z^3, x-2z, 3z^2-2y>

Answer 23

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

Answer 24

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

Answer 25

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

Answer 26

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

Answer 27

i got <2, -1, 1> yes

Answer 28

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

Answer 29

is it right??

Answer 30

is that the plane equation?

Answer 31

i dont have the answer

Answer 32

that is the plane equation

Answer 33

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

Answer 34

the answer isnt an equation...its a value

Answer 35

him; dunno havent read that far yet :)

Answer 36

thats wht m sayin

Answer 37

is the answer 2???

Answer 38

the answer would be 2 then right?

Answer 39

gradient . point

Answer 40

i think so! thanks!

Answer 41

is it 2??

Answer 42

i dont know the value, but it seems right

Answer 43

u understood how it ws done?

Answer 44

i dont think I evenknow how it was done lol

Answer 45

I got -2.

Answer 46

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?

Answer 47

Not entirely sure though.

Answer 48

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

Answer 49

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

Answer 50

so i said

Answer 51

david wht grade u in?

Answer 52

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