Reference no: EM131011106
X2y3z = 30 √(xyz + 2xy + 3z3 - 3) - 18 (2,3,4)
For each surface,
a. Find the equation of the plane tangent to the surface at the given point. Write the equation in the form z - z0 = fx(x0,y0)(x - x0) + fy(x0,y0)(y - y0). Use implicit Differentiation to find fx(x0,y0) and fy(x0,y0). Do not use the shortcut formulas for fx(x0,y0) and fy(x0,y0) that are shown in part b.
b. Find the equation of the plane tangent to the surface at the given point. Write the equation in the form z - z0 = fx(x0,y0)(x - x0) + fy(x0, y0)(y-y0). Use the shortcut formulas to find fx(x0,y0) and fy(x0,y0). That is, use fx(x0,y0) = -Fx/Fz and fy(x0, y0) = -Fy / Fz.
c. Find the equation of the plane tangent to the surface at the given point using gradients. Write the equation in the form ax + by + cx = d.
d. Compare parts (a) - (c) to make sure the equations are the same in all cases.
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