What is the largest output of the function x + yon the ellipse min + y2...
Question 15 1 pts What is the largest output of the function x + y on the ellipse 22 + y2 = 12 4 A) V5 B) 6 C) V7 D) 25 E) 10 OC OA OD OE OB
problems 14 and 15, let R = {(x,y) : x2 + y2 s 2 and y 2 -x}. Sketch the region of integration for the integral: ll -(X+Y) DA -2 -15 -105051 Compute: e-(x+y) dA and show all work.
= 1 is 2 The polar equation of the ellipse x² + y² b2 a 2 b2 1 - e² cos² e Use the above information to write the polar form of the equation of the conic. x2 y2 + 25 16 1 12
3. Compute a potential function for the vecor field V = (x2 + y2 + z2)(x, y, z), and compute the line integral Jov. Tds, where is the straight line segement from point (0,3, 4) to point (3, 4, 12). ind the extremal values of function fm 1 y2) € 21.9.-
8 pts Question 3 Consider the function f(x,y, 2)(x 1)3(y2)3 ( 1)2(y2)2(z 3)2 (a) Compute the increment Af if (r,y, z) changes from (1,2,3 (b) Compute the differential df for the corresponding change in position. What does (2,3,4) to this say about the point (1, 2,3)? ( 13y2)3 ( 1)2(y 2)2(z 3)2 with C (c) Consider the contour C = a constant. Use implicit differentiation to compute dz/Ox. Your answer should be a function of z. (d) Find the unit...
7a please SM 7. Consider the problem min x? - 2x + 1 + y2 - 2y s.t. (x + y) x +y + b = 2/a where a and b are positive constants and x and y are positive. (a) Suppose that (x, y) solves the problem. Show that x and y must then satisfy the equations x = y and 2r'+br = a The equations in () define x and y as differentiable functions of a and b....
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 help with these need working not matlab, thanks. 2 y2 = 1 that is in the 1st quadrant with the counter clockwise 4. C is the portion of ellipse 4 rotation. (a) Express the curve C' in the form of r = x(t)i+y(t)j by using polar coordinate and specify the t value at the starting and the ending points. A2 =2 marks F.dr. where F is the vector function F = (x+y)i+(1-x)j. (b) Evaluate the line integral L =...
Please do #2 40 1. 16 pts) Evaluate the integral( quadrant enclosed by the cirle x + y2-9 and the lines y - 0 and y (3x-)dA by changing to polar coordinates, where R is the region in the first 3x. Sketch the region. 2. [6 pts) Find the volume below the cone z = 3、x2 + y2 and above the disk r-3 cos θ. your first attempt you might get zero. Think about why and then tweak your integral....
1 R 12. Use the transformation T: u = -x and very to evaluate the integral [jx?dA where R is the region bounded on the xy-plane by the ellipse 9x + 4y = 36. . Let S be the image of Runder T on the uv-plane. Sketch regions and S. Set up the integral 7as an iterated integral of a function f(u, v) over region S. Use technology to evaluate the integral. Give the exact answer. R S Y