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Please solve the 3 questions. Question 1: Determine the set of the points at which each...
Determine the set of points at which the function is continuous. f(x, y, z) = 7x + 2y + z D = = x, y, z) | 2 24v 7x + 2y } * Need Help? Read It Talk to a Tutor
All of 10 questions, please. 1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
Please show work on how to solve? (49. Show that the function (x2 +3 for x < 1 f(x) = 10 - x for 1 < x <2 6x - x2 for x > 2 is continuous for x + 1, 2. Then compute the right- and left-hand lim- its at x = 1, 2, and determine whether f is left-continuous, right- continuous, or continuous at these points (Figure 17). y = 10 - x > 9+ y=6x - x2...
Question 1(a&b) Question 3 (a,b,c,d) QUESTION 1 (15 MARKS) Let X and Y be continuous random variables with joint probability density function 6e.de +3,, х, у z 0 otherwise f(x, y 0 Determine whether or not X and Y are independent. (9 marks) a) b) Find P(x> Y). Show how you get the limits for X and Y (6 marks) QUESTION 3 (19 MARKS) Let f(x, x.) = 2x, , o x, sk: O a) Find k xsl and f(x,...
2. Define a function g: R3 +R by g(x, y, z) = 2x2 + y2 + x2 + 2xz – 2y – 4. (a) Find all the critical points of g. (b) Compute the Hessian H, of g. (c) Classify the critical points of g. (d) The surface g(x, y, z) = 0 is an ellipsoid . Use the method of Lagrange multipliers to find the maximum value of the function (5 marks) (5 marks) (5 marks) f(x, y, z)...
1. Find the first and second partial derivatives: A. z=f(x,y) = x2y3 - 4x2 + x2y-20 B. z=f(x,y) = x+ y - 4x2 + x2y-20 2. Find w w w x2 - 4x-z-5xw + 6xyz2 + wx - wz+4 = 0 Given the surface F(x,y) = 3x2 - y2 + z2 = 0 3. Find an equation of the plane tangent to the surface at the point (-1,2,1) a. Find the gradient VF(x,y) b. Find an equation of the plane...
Calculus 3 please answer and show steps to both questions 1. Find the Maximum and minimum values of the following function. 1 f(x, y) x2+y2 + x2y2 Sketch the graph using Maple to verify your calculations. 2. Determine the dimensions of the rectangular box, open the top, having requiring the least amount of material for its a volume of 32 cube-feet and construction. Set up the objective function and constraint. Solving the problem using absolute extremum method. Solving the problem...
Please show step by step how they got (1-4+(9/2))k^2 = 1 on the last line. Find the points on the hyperboloid x2 - y2 + 2z2 = 1 where the normal line is parallel to the line that joins the points (3,-1,0) and (5,3,6). Then f(x,y,z)= x2 - y² + 2z? fe(x,y,z) = 2x 1,(x,y,z) =-2y f:(x, y, z) = 42 Comment Step 3 of 5 A Then yf(x, y, z)=< 2x - 2y, 4z > Let (xo, Yo, 2.)...
please answer step by step Solve the following problem using Lagrange multiplier method: Maximize f(x.y,z) = 4y-2z subject to the constraints 2x-y-z 2 x2+ y2-1 1. (1) (2) (Note: You need not check the Hessian matrix, just find the maximum by evaluating the values of f(x,y,z) at the potential solution points) Also, using sensitivity analysis, find the change in the maximum value of the function, f, if the above changed to: (3) (4) constraints are 2x-0.9y-z 2 x2+y2-0.9. Solve the...
2. For each function, find all critical points and use the Hessian to determine whether they are local maxima, minima, or saddle points. (a) f(x,y,z) = x — 2 sin x – 3yz (b) g(x, y, z) = cosh x + 4yz – 2y2 – 24 (c) u(x, y, z) = (x – z)4 – x2 + y2 + 6x2 – 22