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
the partial derivate of the surface is the gradient, or normal for any given point
grad f . point = equation of the tangent plane
those are the equations for your normal vector components (Fx,Fy,Fz)
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
Fx(x-Px) + Fy(y-Py) + Fz(z-Pz) = 0
Thanks, Im still gettin tripped up with partial derivatives
It didnt come out to be correct, but ill still working on it
i prolly messed the derivatives up somewheres ;) but thats the brunt of it
also, z= would suggest that you solve the end for "z" im assuming
thats what I thought also, it may mean solving for a function as a whole ...meaning z=f(x)
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
z=f(x,y) is what you meant right
I think the problem may be you had (-z) at the end
which would make the problem = to 0 ...not f(x) correct?
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
shuffling and renaming are just conventions for cleaning up the clutter
also, since the z you started with is a surface it wouldnt matter either
wolfram doesnt want to play with it ....
all my partials are good according to the wolf
1.86597+0.144992 x+0.222252 y= z is what I think the wolf simplifies it to
Thats correct! Thanks, wolf ram is such a help
Form your wolf ram link, how did you manage to get the equation...like what section of the page?
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)
it was a hassle even with the wolf, but easier by comparison
awesome, thanks Ill try it out !
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