| -11 points LARCALCET7 14.2.010. Sketch the region and evaluate the terated integrat xY) de 6...
6. [5 marks] Find and classify all stationary points of f(x,y) xy+2xy 7. [6 marks] Sketch the region of integration and evaluate the iterated integral 2 r2 JC 10 (y+xy-2) dxdy. 6. [5 marks] Find and classify all stationary points of f(x,y) xy+2xy 7. [6 marks] Sketch the region of integration and evaluate the iterated integral 2 r2 JC 10 (y+xy-2) dxdy.
sin y 11. Evaluate the integrals Sysin xy dxdy and sketch the corresponding 0 0 region. (10pc
(1 point) Consider the following integral. Sketch its region of integration in the xy-plane. . miten de dy (a) Which graph shows the region of integration in the xy-plane? ? (b) Write the integral with the order of integration reversed: [Ia inte de dy- ." mtej dy de with limits of integration (c) Evaluate the integral (Click on a graph to enlarge it)
To evaluate the following integrals carry out these steps. a. Sketch the original region of integration R in the xy-plane and the new region S in the uv-plane using the given change of variables. b. Find the limits of integration for the new integral with respect to u and v. c. Compute the Jacobian. d. Change variables and evaluate the new integral. х x,y): 0 5x57, 7 sys 6 - -x}; use x=7u, y = 6v - u. S5x25x+7y da,...
u unule question will save this response. Question 11 Evaluate the double integrat: SS (8x?– 4y) da, where R={{x,y) – 15x 53 and 0 sys 1). 6 8 248 3 200 3
5. [-12 Points] DETAILS LARCALCET7 2.2.033.MI. Consider the following. <<2 2 <<4 8 - 2x 6. Sketch the graph of f. 6 2 2 2 4 8 0 10 -10 -6 4 -2 2 -6 y 2 R 2 4 10 -10 0 -6 -2 2 -2 Identify the values of c for which the following limit exists. lim f(x) The limit exists at all points on the graph except where c = 4. The limit exists at all points...
a. Find the Jacobian of the transformation x= 34, y = uv and sketch the region G: 3531 56, 15 uv s 2, in the uv-plane. 6 2 b. Then use -- S S «y dx dy=[[«guw, rus),Mw.v) du dv to transform the integrat $ žay dx into an integral over 6, and evaluate both integrals. R G a. The Jacobian is Choose the correct sketch of the region G below. OC. D. OA. AV 6- 12 b. Write the...
8. Sketch the region of integration and evaluate the integral re dx dy, where G is the region bounded by 0,1, -o,y- 8. Sketch the region of integration and evaluate the integral re dx dy, where G is the region bounded by 0,1, -o,y-
9. (10 points) Evaluate S SR(2x2 - xy - y2)dA, where R is the region bounded by y = -2x +4, y = -2x + 7, y = x - 2, and y = 1 +1.
10. Consider the triangular region R with vertices (0.0) (a) (4 points) Sketch the triangular region R. Vertices (0.0), (0,2), and (4,0) 3/ lebel up, but do not evaluate, an integral for the volume of the solid obtained by rotating the triangular region R abo al (c) (4 points) Set up, but do not evaluate, an integral for the volume of the described solid. The base is the triangular region R. The cross-sections perpendicular to the r-axis are semi-circles with...