Ex.2) Evaluate zdV, where is the solid in the first octant E E bounded by the surface z= = 12xy and the planes y=x, x=1. [Sol.] 0.0 1.0 0.0 -0.5 1.0 y 0.8 06 04 02 GO 0.2 0.6 z = 12xy (graph, level curves) 10 y=x, x=1 z = 12.xy E

Q: Find the area of the surface. The part of the plane x + 2y + 3z = 1 that lies inside the cylinder x²…

A: Solution: If surface 's' has equation of form z= f(x,y) and if 'f' has continous partial…

Q: Let f(x, y) = x² + y?. Then the curve that results from the intersection of the surface z = f(x,y)…

A: When, the surface z=f(x,y) intersects the plane, z=16 , the equation of the resulting surface…

Q: 4. Find the area of the surface generated when the given curve is revolved about the given axis. 3,…

A:

Q: Evalwate f, the inaicated point. (Y.y) and Fy y,y) CY.y) at 3. at (l,3)

A:

Q: 2, z) = 5 and the surfac e at (1,2,3). Evaluate = reasons).

A:

Q: 1.Solve the following polynomial equations.  a)  2X3+1=x2+2X

A:

Q: Find the equation for the tangent plane to the surface z = 6x² - 8y² at the point (2, 1, 16). OA.…

A: NOTE: Refresh your page if you can't see any equations. . so the function f is, the given point…

Q: A surface x(y, z) is defined implicitly xy + yz +x'z' = 3-xZ Calculate ду

A:

Q: 6y dA, R is the quarter-disk in the fourth quadrant enclosed by the curves r+ y = 16, r = =0, and y…

A: Explanation of the answer is as follows

Q: 2. Let f(x, y, z) = ex²-4y²-z². For each of the following, find a value of c so that the level set f…

A:

Q: 4. If the curve y = 3 – x², 0<x<4 is rotated about the y-axis, find the area of the resulting…

A:

Q: Consider the surface given by z = 4x² + y². Draw the level curves for this surface in the (ry) plane…

A: