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du Evaluate dy at (x,y,z)= (2,3,0) for the function (0.0,5) = < Pa cos (); p=51,...
Evaluate Sc (2+2)dy where C is described by parametric equations x(t) = cos(t), y= sin(t), z = 2,0 <t< Select one: O A. +2 O B. 1+2 O C.-1 OD. -1 ABC is a triangle in R where A =(1,4,5), B =(2,-1,0) and C =(4, 2, -3). Find the area of ABC. Select one: O A. (-30,7, -13) O B. -2 OC. V1118 O D. VILLE
Let S be the solid described by the following inequalities: x < 51 – x, 0 < x <y?, and x < y2 < 1. Which of the following represents the volume of S? SL * S dydz do * |* du dydz LL Saz de dy LL. * S dydzde ISL" dedud: S LS du dydz 5 10 1'" dede dy JOJ Let S be the solid bounded by the surfaces z = Vx2 + y2 and z= V1...
F(x, y, z) =< P, Q, R >=<-y +z,x-z,x-y> S: z = 9 - x2 - y2 and z>0 (9a) Evaluate W= $ P dx + Qdy + Rdz с
Evaluate the integral Z π 0 Z π x cos(y) y dy dx. Hint: Since cos(y) y doesn’t have an elementary antiderivative in y, the integral can only be evaluated by reversing the order of integration using Fubini’s theorem.
Question 6 6 pts Suppose that f(x, y, z) is a scalar-valued function and F(x, y, z) = (P(x, y, z), Q(2,y,z), R(x, y, z)) is a vector field. If P, Q, R, and f all have continuous partial derivatives, then which of the following equations is invalid? O curl (aF) N21 = a curl F for any positive integer Q. REC o div (fF) = fdiv F+FVF Odiv curl F = 0 O grad div f = div grad...
Problem 18. 7/2 (1 point) Evaluate the iterated integral AIT cos(x+y+z) dz dx dy. Answer:
q2 please (1) Evaluate the integral (r-1) min(a, y) dy dr, Jo Jo where min(x, y) is the minimum value of r and y. (2) Let f,g : R → R be functions of one variable such that f" and g" are continuous. Show that (f"(x)-g"(y)) dydx = f(0) + g(0)-f(2)-9(2) + 2f'(2) + 2g'(0). o Jo (3) Let a > 0. In spherical coordinates, a surface is defined by r = 2acos φ for 0 φ 1. Find the...
(9) Stokes' Theorem for Work in Space F(x, y, z) =< P,Q,R >=<-y+z, x - 2,x - y > S:z = 4 - x2 - y2 and z>0 (9a) Evaluate W= $ Pdx + Qdy + Rdz с (9) Stokes' Theorem for Work in Space F(x, y, z) =< P,Q,R>=<-y+z, x - 2, x - y > S:z = 4 - x2 - y2 and z 20 (9b) Verify Stokes' Theorem.
6. -1.25 points My Notes Evaluate (y 3 sin x) dx + (z2 +7 cos y) dy x3 dz COS JC where C is the curve r(t) - (sin t, cos t, sin 2t), 0 s t s 27. (Hint: Observe that C lies on the surface z - 2xy.) F dr- 6. -1.25 points My Notes Evaluate (y 3 sin x) dx + (z2 +7 cos y) dy x3 dz COS JC where C is the curve r(t) -...
6. Plot the 3D surface and contour levels of the following function: z(x, y)cos(2y-x) sin(2x) such that-π x π and-r y < π [10 marks] 7. Create a 5 x 5 random matrix M6 with elements ranging from 10 to 33. Using indexing, define the following arrays: An array containing all elements of M6 that are greater than 3 and smaller 6 marks] An array containing all elements of M6 that are negative or between 29 and 33. 6 marks...