Question

Exercise 1. Tangent plane (15 pts) Let (S) be the surface given by the following equation. x+y2 = 1 + z2 An equation of the tangent plane to (S) at A(1,2,2) is: a. 2x + 4y - 4z = 1 b. x +y - z = 0 c. x + 2y – 2z = 1 d. x + y -z = 2 e. None of the above a b d.

Answer 1

= 2n 브 x²+42 = 1+ z² fres 9,2)= x²+42_22_1 AC 1, 2, 2) fre i fy=24 f2=-22 at the given point frect,2,2)=9, fy(1,2,4)= 4 , fz(1,2,3)=-4 The equation of tangent plane is fre(1,2,2)(3-1) + fy (1,2,2)(4-2)+fz642,23(2-2)=0 => ala-1) + 4(4-2) - 4.( 2-2)=0 & send t 24-4-224 426 Ansi ► set 24-22-1=0 => set 24-22=2. Any ② feres 4,2)=x8+2-5 x=rtas , y = ar- sec(s) 2=s 82 called . reaga or ar art yax dr -X2 + y to =260 +25)+ ar- sec(s) =artastar- see(s) Artas seals Ans.