Question

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

Answer 1

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

Answer 2

grad f . point = equation of the tangent plane

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

Thanks, Im still gettin tripped up with partial derivatives

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

shuffling and renaming are just conventions for cleaning up the clutter

Answer 18

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

Answer 19

wolfram doesnt want to play with it ....

Answer 20

there we go:

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

Answer 21

all my partials are good according to the wolf

Answer 22

1.86597+0.144992 x+0.222252 y= z

is what I think the wolf simplifies it to

Answer 23

Thats correct! Thanks, wolf ram is such a help

Answer 24

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

Answer 25

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)

Answer 26

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

Answer 27

awesome, thanks Ill try it out !