Problem 1QC: List the six orders in which the three differentials dx, dy, and dz may be written. Problem 2QC: Write the integral in Example 1 in the orders dx dy dz and dx dz dy. Problem 3QC: Write the integral in Example 2 in the orders dz dy dx and dx dy dz. Problem 4QC: Without integrating, what is the average value of f(x, y, z) = sin x sin y sin z on the cube {(x, y,... Problem 1E: Sketch the region D = {(x, y, z): x2 + y2 4, 0 z 4}. Problem 2E: Write an iterated integral for Df(x,y,z)dV, where D is the box {(x, y, z): 0 x 3, 0 y 6, 0 z ... Problem 3E: Write an iterated integral for Df(x,y,z)dV, where D is a sphere of radius 9 centered at (0,0,0). Use... Problem 4E: Sketch the region of integration for the integral 0101z201y2z2f(x,y,z)dxdydz. Problem 5E: Write the integral in Exercise 4 in the order dy dx dz. 4.Sketch the region of integration for the... Problem 6E: Write an integral for the average value of f(x, y, z) = xyz over the region bounded by the... Problem 7E: Integrals over boxes Evaluate the following integrals. A sketch of the region of integration may be... Problem 8E: Integrals over boxes Evaluate the following integrals. A sketch of the region of integration may be... Problem 9E: Integrals over boxes Evaluate the following integrals. A sketch of the region of integration may be... Problem 10E: Integrals over boxes Evaluate the following integrals. A sketch of the region of integration may be... Problem 11E: Integrals over boxes Evaluate the following integrals. A sketch of the region of integration may be... Problem 12E: Integrals over boxes Evaluate the following integrals. A sketch of the region of integration may be... Problem 13E: Integrals over boxes Evaluate the following integrals. A sketch of the region of integration may be... Problem 14E: Integrals over boxes Evaluate the following integrals. A sketch of the region of integration may be... Problem 15E: Volumes of solids. Find the volume of the following solids using triple integrals. 15.The solid in... Problem 16E: Volumes of solids. Find the volume of the following solids using triple integrals. 16.The solid in... Problem 17E: Volumes of solids. Find the volume of the following solids using triple integrals. 19.The wedge... Problem 18E: Volumes of solids. Find the volume of the following solids using triple integrals. 18.The prism in... Problem 19E: Volumes of solids. Find the volume of the following solids using triple integrals. 22.The solid... Problem 20E: Volumes of solids. Find the volume of the following solids using triple integrals. 20.The wedge... Problem 21E: Volumes of solids. Find the volume of the following solids using triple integrals. 21.The solid... Problem 22E: Volumes of solids. Find the volume of the following solids using triple integrals. 17.The solid... Problem 23E: Volumes of solids Use a triple integral to find the volume of the following solids. 23. The solid... Problem 24E: Volumes of solids Use a triple integral to find the volume of the following solids. 24. The wedge in... Problem 25E: Volumes of solids Use a triple integral to find the volume of the following solids. 25. The wedge of... Problem 26E: Finding an appropriate order of integration Find the volume of the following solids. 36.The solid... Problem 27E: Finding an appropriate order of integration Find the volume of the following solids. 35.The solid... Problem 28E: Finding an appropriate order of integration Find the volume of the following solids. 38.The solid... Problem 29E: Finding an appropriate order of integration Find the volume of the following solids. 37.The solid... Problem 30E: Six orderings Let D be the solid in the first octant bounded by the planes y = 0 and y = x, and the... Problem 31E: Six orderings Let D be the solid in the first octant bounded by the planes y = 0 and y = x, and the... Problem 32E: Six orderings Let D be the solid in the first octant bounded by the planes y = 0 and y = x, and the... Problem 33E: Six orderings Let D be the solid in the first octant bounded by the planes y = 0 and y = x, and the... Problem 34E: Six orderings Let D be the solid in the first octant bounded by the planes y = 0 and y = x, and the... Problem 35E: Six orderings Let D be the solid in the first octant bounded by the planes y = 0, z = 0, and y = x,... Problem 36E: All six orders Let D be the solid bounded by y = x, z = 1 y2, x = 0, and z = 0. Write triple... Problem 37E: Changing order of integration Write the integral 020101ydzdydx in the five other possible orders of... Problem 38E: Triple integrals Evaluate the following integrals. 30.000sinxsinydzdxdy Problem 39E: Triple integrals Evaluate the following integrals. 33.0204y24xdzdxdy Problem 40E: Triple integrals Evaluate the following integrals. 26.0101x201x2y22xzdzdydx Problem 41E: Triple integrals Evaluate the following integrals. 25.0101x201x2dzdydx Problem 42E: Triple integrals Evaluate the following integrals. 28.16042y/30122y3z1ydxdzdy Problem 43E: Triple integrals Evaluate the following integrals. 29.0309z201+x2+z2dydxdz Problem 44E: Triple integrals Evaluate the following integrals. 44. 01y2y02xy15xydzdxdy Problem 45E: Triple integrals Evaluate the following integrals. 31.1ln81zlnyln2yex+y2zdxdydz Problem 46E: Triple integrals Evaluate the following integrals. 32.0101x202x4yzdzdydx Problem 47E: Changing the order of integration Rewrite the following integrals using the indicated order of... Problem 48E: Changing the order of integration Rewrite the following integrals using the indicated order of... Problem 49E: Changing the order of integration Rewrite the following integrals using the indicated order of... Problem 50E: Changing the order of integration Rewrite the following integrals using the indicated order of... Problem 51E: Average value Find the following average values. 51. The average value of f(x, y, z) = 8xy cos z... Problem 52E: Average value Find the following average values. 43.The average temperature in the box D = {(x, y,... Problem 53E: Average value Find the following average values. 45.The average of the squared distance between the... Problem 54E: Average value Find the following average values. 47.The average z-coordinate of points on and within... Problem 55E: Explain why or why not Determine whether the following statements are true and give an explanation... Problem 56E: Changing the order of integration Use another order of integration to evaluate... Problem 57E Problem 58E: Miscellaneous volumes Use a triple integral to compute the volume of the following regions. 54.The... Problem 59E Problem 60E Problem 61E: Miscellaneous volumes Use a triple integral to compute the volume of the following regions. 53.The... Problem 62E: Volumes of solids. Find the volume of the following solids using triple integrals. 24.The solid in... Problem 63E: Two cylinders The x- and y-axes form the axes of two right circular cylinders with radius 1 (see... Problem 64E: Three cylinders The coordinate axes form the axes of three right circular cylinders with radius 1... Problem 65E: Dividing the cheese Suppose a wedge of cheese fills the region in the first octant bounded by the... Problem 66E: Partitioning a cube Consider the region D1 = {(x, y, z): 0 x y z 1}. a. Find the volume of D1.... Problem 67E: General volume formulas Find equations for the bounding surfaces, set up a volume integral, and... Problem 68E Problem 69E: General volume formulas Find equations for the bounding surfaces, set up a volume integral, and... Problem 70E Problem 71E Problem 72E Problem 73E: Hypervolume Find the Volume of the four-dimensional pyramid bounded by w + x + y + z + 1=0 and the... Problem 74E format_list_bulleted
C++ for Engineers and ScientistsComputer ScienceISBN:9781133187844Author:Bronson, Gary J.Publisher:Course Technology Ptr
Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole