Answer to Question #184477 in Calculus for Njabulo

Question

 8. (Sections 2.12, 7.8) Consider the surface S =  (x, y, z) ∈ R 3 | x 2 + y 2 + z 2 = 9 . (a) Define an R 3 − R function f such that S is the contour surface of f at level 9. (1) (b) Use Definition 7.8.6 to find an equation for the plane V that is tangent to S at the point (x, y, z) = (2, 1, 2). (4) (c) Sketch the surface S in R 3 , together with a section of the plane V to illustrate that V is tangent to S at the point (2, 1, 2)

Answer 1

$S=(x,y,z) R^3|x^2+y^2+z^2=9$

(a) $R^3\rightarrow R$

The surface counter surface of f at level -$x^2+y^2+z^2=9$

9.(b) Given point S is  (x, y, z) = (2, 1, 2)

equation for the plane V that is tangent to S is $1(x-2)+1(y-1)+1(z-2)=0$

$x+y+z-5=0$

4.(c) Sketch the surface