Exercise 3. Chain rule (15 pts) Let f(x,y,z) = xy +z-5, x = r + 2s, y = 2r - sec(s),z=s af Then is: ar a. r - sec(s) b. sec(s) c. r+s+sec(s) d. 4r + 4s - sec(s) a. b. d.
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. Exercise 3. Chain rule (15 pts) Let f(x,y,z) = xy...
i need justification please 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 Exercise 3. Chain rule (15 pts) Let f(x,y,z) = xy +z...
Exercise 2. Directional derivative (6 pts + 9 pts) Let f(x, y, z) = xy + y2 – 23 – 105. ... touch 25% 17:12 docs.google.com 2) The direction in which f decreases most rapidly at A(0,1,1) is: a. e. None of the above a. b. C. Exercise 3. Chain rule (15 pts) Let f(x,y,z) = xy +z-5,x=r+2s,y = 2r - sec(s),z=s
Exercise 4. Implicit differentiation (15 pts) Given z - xy + yz + y = 2 and z is a differentiable function in x and y. Then at (1,1,1) is: az дх a. 0 b. 1 1 C 2 d. d e. None of the above a. b. C. d. e. Exercise 6. Double integral in rectangular coordinates (10 pts+10 pts) Let I = S. secx dydx. 1) The region of integration ofl is represented by the blue region in:...
The following common sweetener and dog poison is? (2R, 4R) (2S, 4S) (2R, 3s, 4S) (2R, 3r, 4S] not The following c/s-3(8-dimethylbicyclo[3.2.l]octane is? exo, anti exo, syn endo, anti endo, syri e. not a.-d. The following compound is? E Z both a. and b. not a.-c.
Exercise 4. Implicit differentiation (15 pts) Given z3 – xy + yz + y3 = 2 and z is a differentiable function in x and y. Then at (1,1,1) is: az дх a. 0 b. 1 1 с. 2 d. e. None of the above a. b. e.
Consider the function Let where f(t) is differentiable for all t ∈ R. Show that z satisfies the partial differential equation (x2 − y2 ) ∂z/∂x + xy ∂z/∂y = xyz for all (x, y) ∈ R2 \ { (t, 0)|t ∈ R }.
[5] (2) GIVEN: the surface : x + xy + y + x2 + z = 5 and the point PE 2, P = (1,1,1). FIND: a) (S), and b) The curve, r, shown on 2 ΡεΓcΩ is a curve of points for which y=1, through the point, P. CHECK the sign of az. Does it look correct? ar lp Do
(2) Let f(z, y)-xy +x-y be defined on the closed disk {(z, y) E R2 : z? + y2 < 4} of radius 2. (a) Find the maximu and minimu of Duf at (0,0) over all unit vectors u. (b) Find the maximum and minimum of Duf over all points in the disk(,y) E R2 r2 + y2 < 4} and all unit vectors u. (llint. Think of IvJF as a function ofェand y in the disk.)