Problem 1RCC: Suppose f is a continuous function defined on a rectangle R = [a, b] [c, d]. (a) Write an... Problem 2RCC: (a) How do you define Df(x,y)dA if D is a bounded region that is not a rectangle? (b) What is a type... Problem 3RCC: How do you change from rectangular coordinates to polar coordinates in a double integral? Why would... Problem 4RCC: If a lamina occupies a plane region D and has density function (x, y), write expressions for each of... Problem 5RCC Problem 6RCC: Write an expression for the area of a surface with equation z = f(x, y), (x, y) D. Problem 7RCC Problem 8RCC: Suppose a solid object occupies the region E and has density function (x, y, z). Write expressions... Problem 9RCC: (a) How do you change from rectangular coordinates to cylindrical coordinates in a triple integral?... Problem 10RCC: (a) If a transformation T is given by x = g(u, v), y = h(u, v), what is the Jacobian of T? (b) How... Problem 1RQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,... Problem 2RQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,... Problem 3RQ Problem 4RQ Problem 5RQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,... Problem 6RQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,... Problem 7RQ Problem 8RQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,... Problem 9RQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,... Problem 1RE: A contour map is shown for a function f on the square R = [0, 3] [0, 31. Use a Riemann sum with... Problem 2RE: Use the Midpoint Rule to estimate the integral in Exercise 1. 1. A contour map is shown for a... Problem 3RE: Calculate the iterated integral. 3. 1202(y+2xey)dxdy Problem 4RE: Calculate the iterated integral. 4. 0101yexydxdy Problem 5RE: Calculate the iterated integral. 5. 010xcos(x2)dydx Problem 6RE: Calculate the iterated integral. 6. 01xex3xy2dydx Problem 7RE: Calculate the iterated integral. 7. 00101y2ysinxdzdydx Problem 8RE: Calculate the iterated integral. 8. 010yx16xyzdzdxdy Problem 9RE: Write Rf(x,y)dA as an iterated integral, where R is the region shown and f is an arbitrary... Problem 10RE: Write Rf(x,y)dA as an iterated integral, where R is the region shown and f is an arbitrary... Problem 11RE: The cylindrical coordinates of a point are (23,3, 2). Find the rectangular and spherical coordinates... Problem 12RE Problem 13RE: The spherical coordinates of a point are (8, /4, /6). Find the rectangular and cylindrical... Problem 14RE: Identify the surfaces whose equations are given. (a) = /4 (b) = /4 Problem 15RE: Write the equation in cylindrical coordinates and in spherical coordinates. (a) x2 + y2 + z2 = 4 (b)... Problem 16RE: Sketch the solid consisting of all points with spherical coordinates (, , ) such that 0 /2, 0 ... Problem 17RE: Describe the region whose area is given by the integral 0/20sin2rdrd Problem 18RE: Describe the solid whose volume is given by the integral 0/20/2122sinddd and evaluate the integral. Problem 19RE: Calculate the iterated integral by first reversing the order of integration. 01x1cos(y2)dydx Problem 20RE: Calculate the iterated integral by first reversing the order of integration. 01y1yex2x3dxdy Problem 21RE: Calculate the value of the multiple integral. 21. RyexydA, where R = {(x, y) | 0 x 2, 0 y 3} Problem 22RE: Calculate the value of the multiple integral. 22. DxydA, where D = {(x, y) | 0 y 1, y2 x y + 2} Problem 23RE: Calculate the value of the multiple integral. 23. Dy1+x2dA, where D is bounded by y=x, y = 0, x = 1 Problem 24RE: Calculate the value of the multiple integral. 24. Dy1+x2dA, where D is the triangular region with... Problem 25RE: Calculate the value of the multiple integral. 25. DydA, where D is the region in the first quadrant... Problem 26RE: Calculate the value of the multiple integral. 26. DydA, where D is the region in the first quadrant... Problem 27RE: Calculate the value of the multiple integral. 27. D(x2+y2)3/2dA,where /9 is the region in the first... Problem 28RE: Calculate the value of the multiple integral. 28. DxdA, where D is the region in the first quadrant... Problem 29RE: Calculate the value of the multiple integral. 29. ExydV, where E = {(x, y, z) | 0 x 3, 0 y x, 0 ... Problem 30RE Problem 31RE: Calculate the value of the multiple integral. 31. Ey2z2dV, where E is bounded by the paraboloid x =... Problem 32RE Problem 33RE: Calculate the value of the multiple integral. 33. EyzdV, where E lies above the plane z = 0, below... Problem 34RE Problem 35RE: Find the volume of the given solid. 35. Under the paraboloid z = x2 + 4y2: and above the rectangle R... Problem 36RE: Find the volume of the given solid. 36. Under the surface z = x2y and above the triangle in the... Problem 37RE: Find the volume of the given solid. 37. The solid tetrahedron with vertices (0, 0, 0), (0, 0, 1),... Problem 38RE: Find the volume of the given solid. 38. Bounded by the cylinder x2 + y2 = 4 and the planes z = 0 and... Problem 39RE: Find the volume of the given solid. 39. One of the wedges cut from the cylinder x2 + 9y2 = a2 by the... Problem 40RE: Find the volume of the given solid. 40. Above the paraboloid z = x2 + y2 and below the half-cone... Problem 41RE: Consider a lamina that occupies the region D bounded by the parabola x = 1 y2 and the coordinate... Problem 42RE: A lamina occupies the part of the disk x2 + y2 a2 that lies in the first quadrant. (a) Find the... Problem 43RE: (a) Find the centroid of a solid right circular cone with height hand base radius a. (Place the cone... Problem 44RE Problem 45RE: Find the area of the part of the surface z = x2 + y that lies above the triangle with vertices (0,... Problem 47RE: Use polar coordinates to evaluate 039x29x2(x3+xy2)dydx Problem 48RE: Use spherical coordinates to evaluate 2204y24x2y24x2y2y2x2+y2+z2dzdxdy Problem 49RE Problem 51RE Problem 52RE Problem 53RE: Rewrite the integral 11x2101yf(x,y,z)dzdydxas an iterated integral in the order dx dy dz. Problem 54RE Problem 55RE: Use the transformation u = x y, v = x + y to evaluate Rxyx+ydA where R is the square with vertices... Problem 56RE: Use the transformation x = u2, y = v2 z = w2 to find the volume of the region bounded by the surface... Problem 57RE: Use the change of variables formula and an appropriate transformation to evaluate RxydA, where R is... Problem 58RE: The Mean Value Theorem for double integrals says that if f is a continuous function on a plane... Problem 59RE: Suppose that f is continuous on a disk that contains the point (a, b). Let Dr be the closed disk... Problem 60RE Problem 1P: If [x] denotes the greatest integer in x, evaluate the integral R[x+y]dAwhere R = {(x, y) | 1 x 3,... Problem 2P Problem 3P Problem 4P: If a, b, and c are constant vectors, r is the position vector x i + y j + z k, and E is given by the... Problem 5P Problem 6P: Leonhard Euler was able to find the exact sum of the series in Problem 5. In 1736 he proved... Problem 7P Problem 8P: Show that 0arctanxarctanxxdx=2lnby first expressing the integral as an iterated integral. Problem 9P: (a) Show that when Laplaces equation 2ux2+2uy2+2uz2=0is written in cylindrical coordinates, it... Problem 10P Problem 11P: If f is continuous, show that 0x0y0zf(t)dtdzdy=120x(xt)2f(t)dt Problem 12P: Evaluate limnn2i=1nj=1n21n2+ni+j. Problem 13P: The plane xa+yb+zc=1a0,b0,c0cuts the solid ellipsoid x2a2+y2b2+z2c21 into two pieces. Find the... format_list_bulleted
Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,
Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,