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 2 years ago
Find an equation for the tangent plane to the surface given by\[z=\ln{\left(1+x^2+y^2\right)}\]
 2 years ago
Find an equation for the tangent plane to the surface given by\[z=\ln{\left(1+x^2+y^2\right)}\]

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richyw
 2 years ago
Best ResponseYou've already chosen the best response.0Sorry, at the point (0,2,ln5). why can't I just say\[z_x=\frac{2y}{\left(1+x^2+y^2\right)}\]\[z_y=\frac{2x}{\left(1+x^2+y^2\right)}\]And then that \[zln(5)=z_x(0,2)(x0)+z_y(0,2)(y2)\]

richyw
 2 years ago
Best ResponseYou've already chosen the best response.0so \[z=\frac{4}{5}x+\ln(5)\]

richyw
 2 years ago
Best ResponseYou've already chosen the best response.0I don't see where I am going wrong....

richyw
 2 years ago
Best ResponseYou've already chosen the best response.0nevermind. I see where I went wrong haha.

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.0is it that you don't have the coefficient for z, since you didn't turn it into a function? I want to know because your way is different than mine.

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.0er, I mean didn't turn it into a 3variable function...

richyw
 2 years ago
Best ResponseYou've already chosen the best response.0my notation was sloppy. All I do to find the plane tangent to \(z=f(x,y)\) at the point \(P\left(a,b,f(a,b)\right)\) is use the formula \[zf(a,b)=f_x(a,b)(xa)+f_y(a,b)(yb)\]

richyw
 2 years ago
Best ResponseYou've already chosen the best response.0I just accidentally put f_y where f_x should have been...
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