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...
Change the Cartesian integral to an equivalent polar integral, and then evaluate. 810 PV100 - y2 dx dy -10 - V100 - y2 A) 107 B) 1007 C) 2007 D) 4007 Evaluate the integral. ho 5x + 10y 25° 525-y? j*x + 10% de dx dy to dz dx dy 0 0 A) 625 B) 3125 C) 125 D) 25
11. Use polar coordinates to evaluate the integral 1,8-2V(+ y2)<dy dx
Use Green's Theorem to evaluate the line integral ang the given positively oriented curve (3y+5eVX d(Bx5 cos(y2) dy x2 and x y2 C is the boundary of the region enclosed by the parabolas y Use Green's Theorem to evaluate the line integral ang the given positively oriented curve (3y+5eVX d(Bx5 cos(y2) dy x2 and x y2 C is the boundary of the region enclosed by the parabolas y
Evaluate the iterated integral. 12 [[(x2 - y2) dy dx J-13-2
Change the Cartesian integral to an equivalent polar integral, and then evaluate. ss dx dy -V16-y2 1+122 7:18 +2 1n 5) 2 (8 +2 In 5) 4 (8 + In 5) 78 +in5) 2
Do not evaluate, rewrite the integral using spherical coordinates 25-x² - y2 1 dz dx dy 05 NUS y=0 X-O Z=o
(1 point) Evaluate the integral by changing to cylindrical coordinates. 2 ,2 (a2 +y2)32 dz dy dz 2L,2 (1 point) Evaluate the integral by changing to cylindrical coordinates. 2 ,2 (a2 +y2)32 dz dy dz 2L,2
Evaluate the line integral. fr de x² dx + y²dy, where C is the arc of the circle x2 + y2 = 4 from (2,0) to (0,2) followed by the line segment from (0, 2) to (4,3).
Evaluate the integral. 2 V4-y2 aproba o por con 2x+4y dz dx dy