Problem 1QCE: Let T be the transformation from the u-plane to the xy-plane defined by the equations x=u2,y=3u+ (a)... Problem 2QCE: State the relationship between R and S in the change of variables formula... Problem 3QCE Problem 4QCE: The Jacobian of the transformation x=u,y=w,z=2w is x,y,zu,,w= Problem 1ES: Find the Jacobian x,y/u,. x=u+4,y=3u5 Problem 2ES: Find the Jacobian x,y/u,. x=u+22,y=2u2 Problem 3ES Problem 4ES: Find the Jacobian x,y/u,. x=2uu2+2,y=2u2+2 Problem 5ES: Solve for x and y in terms of uand, and then find the Jacobian x,y/u,. u=2x5y,=x+2y Problem 6ES Problem 7ES Problem 8ES Problem 9ES: Find the Jacobian x,y,z/u,,w. x=3u+,y=u2w,z=+w Problem 10ES: Find the Jacobian x,y,z/u,,w. x=uu,y=uuw,z=uw Problem 11ES Problem 12ES Problem 13ES: Determine whether the statement is true or false. Explain your answer. If r=xu,i+yu,j, then... Problem 14ES Problem 15ES Problem 16ES Problem 17ES: Sketch the image in the xy-plane of the set S under the given transformation. Problem 18ES Problem 19ES: Sketch the image in the xy-plane of the set S under the given transformation. Problem 20ES: Sketch the image in the xy-plane of the set S under the given transformation. Problem 21ES: Use the transformation u=x2y,=2x+y to find Rx2y2x+ydA where R is the rectangular region enclosed by... Problem 22ES: Use the transformation u=x+y,=xy to find Rxyex2y2dA over the rectangular region R enclosed by the... Problem 23ES Problem 24ES Problem 25ES: The transformation x=au,y=ba0,b0 can be rewritten as x/a=u,y/b=, and hence it maps the circular... Problem 26ES Problem 27ES: The transformation x=au,y=ba0,b0 can be rewritten as x/a=u,y/b=, and hence it maps the circular... Problem 28ES: Show that the area of the ellipse x2a2+y2b2=1 is ab. Problem 29ES: If a, b, and c are positive constants, then the transformation x=au,y=b,z=cw can be rewritten as... Problem 30ES Problem 31ES: Find a transformation u=fx,y,=gx,y that when applied to the region R in the xy-plane has as its... Problem 32ES: Find a transformation u=fx,y,=gx,y that when applied to the region R in the xy-plane has as its... Problem 33ES: Find a transformation u=fx,y,=gx,y that when applied to the region R in the xy-plane has as its... Problem 34ES: Find a transformation u=fx,y,=gx,y that when applied to the region R in the xy-plane has as its... Problem 35ES Problem 36ES: Evaluate the integral by making an appropriate change of variables. Rx2y2dA, where R is the... Problem 37ES: Evaluate the integral by making an appropriate change of variables. Rsinxycosx+ydA, where R is the... Problem 38ES: Evaluate the integral by making an appropriate change of variables. Reyx/y+xdA, where R is the... Problem 39ES: Use an appropriate change of variables to find the area of the region in the first quadrant enclosed... Problem 40ES: Use an appropriate change of variables to find the volume of the solid bounded above by the plane... Problem 41ES: Use the transformation u=x,=zy,w=xy to find Gzy2xydV where G is the region enclosed by the surfaces... Problem 42ES: Use the transformation u=xy,=yz,w=xz to find the volume of the region in the first octant that is... Problem 43ES: (a) Verify that a1b1c1d1a2b2c2d2=a1a2+b1c2a1b2+b1d2c1a2+d1c2c1b2+d1d2 (b) If x=xu,,y=yu, is a... Problem 44ES: The formula obtained in part (b) of Exercise 43 is useful in integration problems where it is... Problem 45ES: The formula obtained in part (b) of Exercise 43 is useful in integration problems where it is... Problem 46ES: The formula obtained in part (b) of Exercise 43 is useful in integration problems where it is... Problem 47ES: The three-variable analog of the formula derived in part (b) of Exercise 43 is x,y,zu,,wu,,wx,y,z=1... Problem 48ES: (a) Consider the transformation x=rcos,y=rsin,z=z from cylindrical to rectangular coordinates where... Problem 49ES Problem 50ES format_list_bulleted