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Changing the Order of
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EBK MULTIVARIABLE CALCULUS
- Flow in an ocean basin An idealized two-dimensional ocean is modeled by the square region R = - x - with boundary C. Consider the stream function (x, y) = 4 cos x cos y defined on R (see figure). yA 3 a. The horizontal (east-west) component of the velocity is u = 4, and the vertical (north-south) component of the veloc- ity is v = -, Sketch a few representative velocity vectors and show that the flow is counterclockwise around the region. b. Is the velocity field source free? Explain. c. Is the velocity field irrotational? Explain. d. Let C be the boundary of R. Find the total outward flux across C. e. Find the circulation on C assuming counterclockwise orientation.arrow_forwardChanging order of integration Write the integral ∫20 ∫10 ∫1-y0 dz dy dx in the five other possible orders of integration.arrow_forwardtrue or false?arrow_forward
- Puestion 2x*+ 2x + 1 Examine x²+5x for ylo6) by RK-4 meathodify(0)=1, h=0.2.arrow_forwardEvalule the Integral -3x dz |arrow_forwardIntegral Calculus - Plane Area 1. Find the area in the first quadrant enclosed by y = (x2 + 4)/x2, x = 2 and x = 4, using a vertical element. EXPLAIN AND SHOW FULL SOLUTION.arrow_forward
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