Find the planes tangent to the following surfaces at the indicated points.

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Find the planes tangent to the following surfaces

Answer

Consider the following equation of the surface Given point: 1,2, Let ,f(x,y,z)=x + 2y +3xz-10 The gradient of the surface i

The vector n is normal to the given surface is (3,8,3 The equation of the plane is 9(-1)+86-2)+3 3x+8y +3z 3-16-1 0 3x+8y + 3

小匙2-/-3) oz 3 Oz oz oz = 0-0-0 0 2 12,8 The vector n is normal to the given surface is (12.8) = (- The equation of the plane

-2(x-1) +4(y-2)-0(z-8)=0 -2x+ 2+4y-8 0 2x-4y +6 = 0 Consider the following equation of the surface nz = 1 Given point: (1.1,1

The vector n is normal to the given surface is, n (Vfan (LLl) 1,1,1 The equation of the plane is, x1-1+1(z-1) 0 xtytz-30

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