1. Given z = x+(y-3) -9. i) Determine the domain and range of the function. (2...

  

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1. Given z = x+(y-3) -9. i) Determine the domain and range of the function. (2 marks) ii) Sketch the level curve of the function for z = 0 and z = 7. (3 marks) 2. Sketch the level surface of the function for w = 4. f(x,y,z) =w=4x + y (4 marks) 1 dw 3. Find by using chain rule where w = ln(x + 2y - 2), x = 2t - 1, y = dt and z = t. x+y 4. Let w 2-z' x=2rs, y = sin(rt) and z = st. Find rule when r = 4, s = 2 and t = 0. (6 marks) by using chain (5 marks) 5. Let z be defined implicitly as a function of x and y by the equation x cosech y + z = x+ 2x2 y z Find (5 marks) xy 6. Predation of species y on species x is governed by P(x,y) = 1x Approximate the change in predation if x increases from 100 to 105 and y decreases from 5 to 4 by using total differential. (6 marks) 7. Given (1,1), (0,0), (0, 2), (-1, 1) are the critical points of the function f(x, y) = ax2y+y-3x- by. Find the values of a and b. Then determine whether each of the critical point is a local maximum, a local minimum or a saddle point. (9 marks) 1. Given z = x+(y-3) -9. i) Determine the domain and range of the function. (2 marks) ii) Sketch the level curve of the function for z = 0 and z = 7. (3 marks) 2. Sketch the level surface of the function for w = 4. f(x,y,z) =w=4x + y (4 marks) 1 dw 3. Find by using chain rule where w = ln(x + 2y - 2), x = 2t - 1, y = dt and z = t. x+y 4. Let w 2-z' x=2rs, y = sin(rt) and z = st. Find rule when r = 4, s = 2 and t = 0. (6 marks) by using chain (5 marks) 5. Let z be defined implicitly as a function of x and y by the equation x cosech y + z = x+ 2x2 y z Find (5 marks) xy 6. Predation of species y on species x is governed by P(x,y) = 1x Approximate the change in predation if x increases from 100 to 105 and y decreases from 5 to 4 by using total differential. (6 marks) 7. Given (1,1), (0,0), (0, 2), (-1, 1) are the critical points of the function f(x, y) = ax2y+y-3x- by. Find the values of a and b. Then determine whether each of the critical point is a local maximum, a local minimum or a saddle point. (9 marks)