The tangent plane equation of tangent plane is
z = x - 6y -1
This is further explained below.
What is the equation of the tangent plane to the surface z=ln(x-6y) at the point(7,1,0)?
Generally, Given surface is z = ln(x − 6y) ,
Given point is = (7, 1, 0)
partially differentiating with respect to x
== >zx = [1/(x - 6y)] (1) = 1/(x - 6y)
zx (7 , 1 , 0) = 1/(7 - 6(1)) = 1
Partially differentiating with respect to y
zy = [1/(x - 6y)] (-6)
zy = -6/(x - 6y)
zy(7 , 1 , 0) = -6/(7 - 6(1)) = -6
Equation of tangent plane is z - = zx(x -
) + zy(y -
)
z - 0 = 1(x - 7) + (-6)(y - 1)
z = x - 7 -6y + 6
z = x - 6y -1
In conclusion, equation of tangent plane is z = x - 6y -1
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