2. Use the Divergence Theorem to evaluate JJ Fas where F= (sin(x), zy³, z2 + 4x) and S is the surface of the box with -1 < x≤ 2,0 ≤ y ≤ 1,1 ≤ 2 ≤4.

Q: Consider the right triangle withvertices (0, 0), (0, b), and (a, 0), where a &gt; 0 and b &gt; 0.…

A: Given right angle triangle has vertices  (0, 0), (0, b), and (a, 0), where a &gt; 0 and b &gt; 0.…

Q: Find Əz ?х Əz da Əz ду = ab brackets (e.g. x*y rather than xy; 2*(x+y) rather than 2(x+y)). • Put…

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Q: Find the extreme values of the function f(x,y,z) = 9xy + 6z² on the circle in which the plane y - x…

A: The given function is fx, y, z=9xy+6z2. The equation of the plane is y-x=0. The equation of the…

Q: Let r(t) be a positively oriented rectangle with corners (0,0), (0,1), (2,1) and (2,0) and F(r, y)…

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Q: Sketch the surface 1≤z≤ √9-x² - y² 1≤z≤√9-x² - y² and_x² + y² ≤1

A: Given is the surface surface 1≤z≤9-x2-y2 and x2+y2≤1 The objective is to sketch this surface.…

Q: Q1// Evaluate , F ds where F = yi + xj + 4zk and S is the surface x? + y? = 9 in the first octant…

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Q: The horizontal tangent plane of the surface z = 4x – xy – 2y – 2x – 8y – 3 is given by the equation…

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Q: Use the Divergent Theorem to find all values of b> −1 such that ∫∫SFdS = (45b/2) + (51/2), where F…

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Q: the plane for (x³ - x²y)dx + xy²dy], where (C) is the boundary of the region enclosed by the circler

A: The solution is given by

Q: ve = Vti + Vrj + (2t – 1)k is tangent to the surface x+y-z = 1 Show that the curv when t=l

A: Consider the given curve r=ti+tj+2t-1k And the given surface x2+y2-z=1 First, write the curve in…

Q: Solve the D. E. to the I. V. P. sinx(e-y + 1)x' – cosx = 1, y(0) = 0 %3D %3D (1 – e') (1 + cos.x) =…

A: We will find out the required solution.

Q: 4. Use Stokes' Theorem to evaluate [ F• dr when z = 4-y F(x, y. 2)= xz° 7+(x+z*)7+ -x |k. Let C is…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: 1) Prove Green's Theorem for F = 3xy'i - 4xj around the curve C bounded %3D 160 by y = 2x and y =…

A: These questions are about green's theorem around any given curve c.

Q: Show that the function given by f(x,y)= x² + 3xy is differentiable at every poin using the…

A: Introduction: Distinctiveness (differentiability) implies continuity. If a function is…

Q: If F(x, y, z) = xzi+3ryj-2zk, evaluate fF.dS using Gauss's theorem when S is the closed cylinder…

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Q: Sketch the surface 1≤z≤√√9-x²-y²_and_x² + y² ≤

A: Solution is below

Q: s) Given u(r, s) =r2 - 2s2, wheter= and s = y? - r, compute for du

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Q: F. dS, where F(x, y, z) = z²xi + 2) + (x2z + y2)k and S is the top half of the sphere x² + y² + z? =…

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Q: 3 Find the Minimum distance from the origin to the plane X+2y-z=5

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Q: Encik Samsudin, a PhD student has reported the concentration of E.coli bacteria, C(μg/L) in a…

A: Given: C=kmaxt25+2t2+3.5t To find the root and to determine the fastest time for the E.coli…

Q: Consider f (x, y) 3x² + xy + 3y². Use calculus to find the extreme values of fon the circle x² + y²…

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Q: Calculate SS dxdy D (x+y)² in Surface D limited to curve y=x² and the lines 2 Y=x+2 and x = 1.

A: Given:  integral ∫∫Ddxdy(x+y)2  in the surface D limited to curve y=x2 , y=x+2, x=1  To Find : value…

Q: Sketch the domain D in the (x, y)-plane satisfying ≤ y ≤ 2e- and e ≤ y ≤ 3e. In your sketch, label D…

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Q: Exercise 5. Compute F F.NdS where F(x, y, z) surface of the plane x + 2y + z = 6 in the first…

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Q: b) Use Gauss' theorem to evaluate RR F. ndS where F = (x² - y)i + y³z²j + (xy – y²z³)k UTM UTM and o…

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Q: Find √x²ds ds along the line of intersection of the two planes x-y+z=0 and x+y+2z=0, from origin to…

A: The two given planes are x-y+z=0 and x+y+2z=0.