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Mathematics 64 Online
OpenStudy (anonymous):

Find the equation of the tangent plane to the surface z=e^(1x/17)*ln(4y) at the point (−2,4,2.465). z = Find the equation of the tangent plane to the surface z=e^(1x/17)*ln(4y) at the point (−2,4,2.465). z = @Mathematics

OpenStudy (amistre64):

the partial derivate of the surface is the gradient, or normal for any given point

OpenStudy (amistre64):

grad f . point = equation of the tangent plane

OpenStudy (amistre64):

\[F(x,y,z)=e^{x/17}*ln(4y)-z\] \[Fx=\frac{1}{17}e^{x/17}*ln(4y)\]\[Fy=e^{x/17}*\frac{1}{y}\]\[Fz=-1\]

OpenStudy (amistre64):

those are the equations for your normal vector components (Fx,Fy,Fz)

OpenStudy (amistre64):

apply the values from the given point and you got the normal to the curve at that point; then its just a matter of plugging in the rest

OpenStudy (amistre64):

Fx(x-Px) + Fy(y-Py) + Fz(z-Pz) = 0

OpenStudy (anonymous):

Thanks, Im still gettin tripped up with partial derivatives

OpenStudy (anonymous):

It didnt come out to be correct, but ill still working on it

OpenStudy (amistre64):

i prolly messed the derivatives up somewheres ;) but thats the brunt of it

OpenStudy (amistre64):

also, z= would suggest that you solve the end for "z" im assuming

OpenStudy (anonymous):

thats what I thought also, it may mean solving for a function as a whole ...meaning z=f(x)

OpenStudy (amistre64):

its the same really, the xyzs all come out in the end; its just easier to work it from the F(x,y,z) setup i believe

OpenStudy (amistre64):

z=f(x,y) is what you meant right

OpenStudy (anonymous):

I think the problem may be you had (-z) at the end

OpenStudy (anonymous):

which would make the problem = to 0 ...not f(x) correct?

OpenStudy (amistre64):

spose you had something normal looking like: y = x^2 then 0 = x^2 -y is the same set up and can be called by another function: f(x,y) = x^2-y

OpenStudy (amistre64):

shuffling and renaming are just conventions for cleaning up the clutter

OpenStudy (amistre64):

also, since the z you started with is a surface it wouldnt matter either

OpenStudy (amistre64):

wolfram doesnt want to play with it ....

OpenStudy (amistre64):

there we go: http://www.wolframalpha.com/input/?i=e^%281x%2F17%29*ln%284y%29

OpenStudy (amistre64):

all my partials are good according to the wolf

OpenStudy (amistre64):

1.86597+0.144992 x+0.222252 y= z is what I think the wolf simplifies it to

OpenStudy (anonymous):

Thats correct! Thanks, wolf ram is such a help

OpenStudy (anonymous):

Form your wolf ram link, how did you manage to get the equation...like what section of the page?

OpenStudy (amistre64):

i checked my partials by simply typing in d/dx (equation) and those checked out, soo all i had to do was take those partials and insert the point info, then typed in simplify (messey equation)

OpenStudy (amistre64):

it was a hassle even with the wolf, but easier by comparison

OpenStudy (anonymous):

awesome, thanks Ill try it out !

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