$*$*-* ? /12-** Rewrite the following integral using the order dydxdz (4 - x)/2 (12-3x -6y)/4...
For the described solid S, write the triple integral f(x,y, z)dV as an iterated integral in (i) rectangular coordinates (x,y, z); (ii) cylindrical coordinates (r, 0, 2); (iii) spherical coordinates (p, φ,0). a. Inside the sphere 2 +3+224 and above the conezV b. Inside the sphere x2 + y2 + 22-12 and above the paraboloid z 2 2 + y2. c. Inside the sphere 2,2 + y2 + z2-2 and above the surface z-(z2 + y2)1/4 d. Inside the sphere...
5. Express the triple integral | f(x,y,z)dV as an iterated integral in cartesian coordinates. E is the region inside the sphere x2 + y2 + z2 = 2 and above the elliptic paraboloid z = x2 + y2
SOLVE THE FOLLOWING SYSTEM OF EQUATIONS BY THE CRAMER'S METHOD 3X+5Y+3Z-12 2X+5Y-2Z-6 3x+6Y+3Z-3 a) X Y b) CHECK YOUR RESULTS. (USE MATRICE FUNCTIONS, PRESS F2. AND THEN PRESS CTRL+SHIFT+ENTER) 3IF Y-SINC) EXPOO. INTEGRATE Y FROM X-0 Tox-1. COMPARE WITH REAL VALUE IF DX-0 a) INT b) INT ,IF DX- 005 REAL VALUE 3) Plot sin x letting maco c/ Prepave hese cuves 4) SOLVE THE FOLLOWING SYSTEM OF EQUATIONS BY INVERSE METHOD 3 X+3Z-13 2X +5 Y-2Z-2 3 X+6Y+2Z-3 Z-...
2 x-I 3. Find the volume of solids enclosed by a paraboloid z x2+ y2 and an x2y2+z2 =6 ellipsoid 4 Sud, a.
2 x-I 3. Find the volume of solids enclosed by a paraboloid z x2+ y2 and an x2y2+z2 =6 ellipsoid 4 Sud, a.
Which vector points in the direction in which one should travel in order to experience the greatest rate of change of the function g(x, y, z) = xy + 5 yz’if one is currently located at the point (3,2,4)? 7) 8î +116j+80k b) 2-129 + Â €) -7 - 5j + 46k d)84i+j-51 e) none of these I The intersection of the graphs of f(x, y) = 5x+y+43-6 and = = 64 is a level curve of the function f....
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....
Find the extreme values of the function f(x, y) = 3x + 6y subject to the constraint g(x, y) = x2 + y2 - 5 = 0. (If an answer does not exist, maximum minimum + -/2 points RogaCalcET3 14.8.006. Find the minimum and maximum values of the function subject to the given constraint. (If an answer does not exist, enter DNE.) f(x, y) = 9x2 + 4y2, xy = 4 fmin = Fmax = +-12 points RogaCalcET3 14.8.010. Find...
(1 point) Evaluate the surface integral || (3x yi – 3yzj + zxk) · dS. JJ s . Where S is the part of the paraboloid z = 9 – x2 - y2 that lies above the square 0 < x < 2, 0 < y < 1, and has upward orientation. X2 / 2 (3xyi – 3yzj + zxk) · dS = JJS 9-x^2-y^2 Σ dy dx J xi Jyi where M M O-ON x1 = M M Evaluate...
Maximize p = 3x + 6y + 3z + 6w + 3v subject to x + y ≤ 3 y + z ≤ 3 z + w ≤ 9 w + v ≤ 12 x ≥ 0, y ≥ 0, z ≥ 0, w ≥ 0, v ≥ 0. p = (x,y,z,w,v)=
a - e
(a) X + y +z = 11 X – Y – 2= -3 -2 + y - 2 = 5 (3x – y + 2z = 2 (b) x+y+z+t+p=17 X - Y - 2-t-p= -5 z +t+ p + y = 11 p - x - y = 1 -t + x = 10 (c) x +y + 2+t= -6 X - Y - 2 -t = 20 y - X=-39 2x + 3t + y -...