Exercise 4. Implicit differentiation (15 pts) Given z3 – xy + yz + y3 = 2...
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:...
Let f(x,y,z) = xy + z-5,x=r +2s, y = 2r - sec(s), z = s Then I is: ar a. r - sec(s) b. sec(s) c. r+s+sec(s) d. 4r + 4s - sec(s) a. b. C. Given zº – xy + y2 + y2 = 2 and z is a differentiable function in x and y. Then at (1,1,1) is: дх a. 0 b. 1 c. d. e. None of the above o a. o b. ♡ C. o d.
(5 pts) b. Use implicit differentiation to find z, if yz = ln(x + z). I
Question 15 Use implicit differentiation to find if: x In(y + 2) + y2 = 0 дх Ay+2 + x2 y + x2 + x2 8.-(4+2) In(y + 2) x + y + y2 C. None of the answers D. (x + 2) In(x + 2) y + x2 + x2 E-(*+7+42 x + y2 + y2
Question 15 4 pts Use implicit differentiation to find the specified derivative at the given point. az Find at the point (6, 1,-1) for In exy+z2 = 0 6e7-1 1-2e 2e7- 1-6e O 1-2e 1-6e7 1-6e7 1-2e7 Question 15 4 pts Use implicit differentiation to find the specified derivative at the given point. az Find at the point (6, 1,-1) for In exy+z2 = 0 6e7-1 1-2e 2e7- 1-6e O 1-2e 1-6e7 1-6e7 1-2e7
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 1. Tangent plane (15 pts) Let (5) be the surface given by the following equation. x2+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. C. O d. e. Exercise 2. Directional derivative (6 pts + 9 pts)...
Question 22 4 pts Find the sum-of-prime-implicants form of the following Boolean expression: xy +2'z+yz' + xyz xy + xz+y O xy + y2 + 2 OX'z+y+z' O2 + y + 2 None of the above.
15 PTS) 2. Use implicit differentiation to show that x + y +exy = 0 is an implicit solution to the nonlinear equation (1 + xexy)*%+1+ yexy = 0. dx
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...