(a) (2 points) In the plane below, sketch the region corresp below, sketch the region corresponding...
3. See NumSys Practice Class 10.] Sketch the following regions in the complex plane. Re- member to mark boundaries appropriately with solid lines or dashed lines according to whether or not the boundary itself is contained in the region. Mark all points of intersection of the boundaries with the real and imaginary axes. Draw a separate diagram for each part For part (d), if a point simultaneously lies upon a dashed line and a solid line, mark it with either...
2. (a) Sketch the region of integration and evaluate the double integral: T/4 pcos y rsin y dxdy Jo (b) Consider the line integral 1 = ((3y2 + 2mº cos x){ + (6xy – 31sin y)ī) · dr where C is the curve connecting the points (-1/2, 7) and (T1, 7/2) in the cy-plane. i. Show that this line integral is independent of the path. ii. Find the potential function (2, y) and use this to find the value of...
The solid S sits below the plane z = 2x + 5 and above the region in the xy-plane where 1 < x2 + y2 = 4 and x + y < 0. The volume of S is:
Sketch the region corresponding to the statement PC - c<z<c) = 0.6. Shade: Left of a value Click and drag the arrows to adjust the values. . +++++++++ 4 -3 0 -2 1-7 -1.5 2
3. (a) If the region sketched in (1) above is revolved about the line y -0 (x-axis), sketch and label the typical rectangle(s) needed to use the shell method to find the volume of the resulting solid. (b) Use the shell method to find the volume of the resulting solid 2 pts [9 pts] 4. (a) If the region sketched in (1) above is revolved about the line x-O。-axis), sketch and label the typical rectangle(s) needed to use the disk/washer...
1. Sketch the region in the complex plane that contains the elements of {Z – 3+i:ze C,1<\2-11 <2} n {z EC: Im(2) >0}. Justify your answer.
Q1: What are the indices for the two planes drawn in the sketch below? +z Plane 1 Plane 2 +y 0.3 nm 0.6 nm -0.6 nm +x Solution: (only inside the table) Plane 1 y. 2 Intercepts Intercepts in terms of a, b, and с Reciprocals of intercepts Enclosure Plane 2 X Y. Z Intercepts Intercepts in terms of a, b, and с Reciprocals of intercepts Enclosure Q2: The accompanying figure shows three different crystallographic planes for a unit cell...
Please help me solve these im really struggling. thanks ! 1. (20 points) Sketch the region bounded by the graphs of the equations and find the area of the region: x = f(y) = y2 + 1, X = g(y) = 0, y=-1, y = 2 2. (30 points) Find the volume of the solid generated when the region in Quadrant | bounded by these equations is revolved about the line x =3. y= 9 – x², x > 0,...
12. Consider the region bounded above by the function ?=1/(?+2)2(?+6)^2 and below by the xy-plane for x≥0 and ?≥0. (1 point) Consider the region bounded above by the function z = - "2" (x + 2)2(y + 62 an and below by the xy-plane for x > 0 and y 2 0. On a piece of paper, sketch the shadow of the region in the xy-plane. Set up double integrals to compute the volume of the solid region in two...
Use a change of variables to find the volume of the solid region lying below the surface -f(x, y) and above the plane region R x, y)xy)e- R: region bounded by the square with vertices (4, 0), (6, 2), (4, 4), (2, 2) Use a change of variables to find the volume of the solid region lying below the surface -f(x, y) and above the plane region R x, y)xy)e- R: region bounded by the square with vertices (4, 0),...