Math  /  Calculus

QuestionConsider the surface at the point P(0,3,0)P(0,3,0). 4z+3=9e9xycos(z)4 z+3=9 e^{9 x} \cdot y \cdot \cos (z) a. Choose the correct equation for the tangent plane to the surface at that point. 243x+9y4z27=0243 x+9 y-4 z-27=0 b. Find a vector v\mathbf{v} that is normal to the surface at that point.

Studdy Solution
Verify the given tangent plane equation:
The given equation is 243x+9y4z27=0 243x + 9y - 4z - 27 = 0 , which matches our derived equation.
The correct equation for the tangent plane is 243x+9y4z27=0 243x + 9y - 4z - 27 = 0 , and a normal vector to the surface at the point is v=243,9,4 \mathbf{v} = \langle -243, -9, 4 \rangle .

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