Question

QUESTION 1 Find an equation for the tangent plane and normal line to the surface f(x, y, z)= z - 2e-* cos y at the point P. (0,1,1) (4 marks)

Answer 1

Griven surface is 1619,9,2)= 7-28 ExCopy Now 2319,9,7) ze">Copy af(x,y,z) ay 2e "Siny af(x,y,z) 2Z aflot, D ze cos a 22 .2 28(0,7, 1) ze seina ay of (0,0,1) =) 27 The rebone the equation of the tangent plane to the surface at the point Polon, i) is la-o) 2310,7,1) +(9-70) 2840,7,1) +7-1) 2-(0,2,1) 29 , (2-0) X(-2) +(y-7) xo +(3-1)x1=0 om 22-7+1=0 22 az

The to the parametric equations surface at the 2*10,0,1) of the normal tine point Polon, 1) are 210,2,1) 2z x = 0++. y=x+to Za 1+t. 21(0,7,1) 22 ay z=1+txt That is 220 +tx(-2) y aattxo ie. x = -27 y = 7, 7-5+1 where t is a parameter