5. For F(X, Y,Z)- 2m(2,3,6,7): pointe) CoautraKah a o the function (b) (3 points) List all...
Q3: 1. For the Boolean function shown below, answer the questions F(W,X,Y,Z) = 11 (6,8,9,10,11,12,13) use K-MAP to: • Derive the BF as SOP. • Derive the BF as POS. • Find All prime implicants of the BF. • Determine the Essential prime implicant(s). 2. Let the BF change to have don't care condition as: F(W,X,Y,Z) = 1,3,7,11,15 + de E(0.2,5) Derive the BF as SOP and POS.
(a) Find and classify all of the critical points of the function X f(x, y, z) = (x2 +42 + x2)3/2 on the unit sphere. (b) Find and classify all of the critical points of the function f(x, y, z) = x sin(x2 + y2 +22) on the sphere of radius
5. (7 points) Let f: R3 → R be the function f(x,y,z) = x2 + y2 +3(2-1)2 Let EC R3 be the closed half-ball E = {(x, y, z) e R$: x² + y2 +< 9 and 2 >0}. Find all the points (x, y, z) at which f attains its global maximum and minimum on E.
Homework 4: Problem 3 Previous Problem Problem List Next Problem (6 points) Consider the function f(x, y) - (e - x) sin(y). Suppose S is the surface z- f(x, y) (a) Find a vector which is perpendicular to the level curve of f through the point (5,5) in the direction irn which f decreases most rapidly. vector (b) Suppose u = 31 + 3/4 ak is a vector in 3-space which is tangent to the surface S at the point...
Identify all essential prime-implicants of the function f(A,B,C,D) = (0,2,4,5,6,8,10,13,15) and find all minimal functions. Please show steps.
Problem 4 [10 points] For the functions below, draw their Kmaps and indicate their prime implicants and essential prime implicants. Then write down their simplified form. Make sure it is easy to distinguish them using different colors or other clear markings. (a) F(x, y, z, w)- (1, 5, 7, 8, 9, 12, 13, 14, 15) (b) G(r, y, z, w)- (0,2,3,4,5, 8, 10, 11, 13, 15)
Problem 1: Find all of the essential prime implicants for the following Boolean functions (d) F = y,z + wyz + w,(y' + z')
uestion Completion Status QUESTION 1 What are the essential prime implicants for the logic function fa,b,c,d) □ blcd Σ m(2,3,5,6,7, 10, 11, 13, 14)? labd □cid lac QUESTION 2 A minimum cost SOP cover will include? O Some of the essential prime implicants O Only the essential prime implicants O All of the essential prime implicants Clich Save and Submit to save and submit Click Save All Answers to save all answers
rty. I 5. [16 pointsj Consider the function f(x, y,z) Let S denote the level surface consisting of all points in space such that f(,y,z)-4, and let P- (2,-2,1), which is on S. a) Calculate Vf. b) Determine the maximum value of Daf(P), where u is any unit vector at P c) Find the angle between Vfp and PO, where O denotes the origin. d) Find an equation for the tangent plane to S at P rty. I 5. [16...
(1 point) Consider the function f(x, y) = 4x+ + 8y. List all critical points of f(x, y). If there are none, enter "none". If there is more than one, enter a comma-separated list of ordered pairs, e.g., "(1,2), (3,4). (5,6)" Critical points are List all critical points of f(x,y) which are local maxima. If there are none, enter "none". If there is more than one, enter a comma-separated list of ordered pairs, e... "(1,2), (3,4), (5,6) Local maxima occur...