Let E be the hemisphere described by Oszs V1-x? -y2 and F=Vz? + x2 + y² i+Vz? + x² +v² j+Vz? + x² +y² x? +1 Compute F. Nds DE Select one: а. TT TT 3 2 d. TT 4 e. Non of them b.

Q: 4) For which one of these linear maps T:R → R? is det T > 0? a) T(1, y) = (y, -r) b) T(1, y) = (x,…

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Q: 1. Let S be the part of the cone z? = x? +y² that lies between the planes z = 1 and z = 2. Compute…

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Q: 5) Compute J(x²+y?)dxdy, where D is the intersection of c irc les r=2 cosg and =2sing.

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A: The equation of the parametric curve (path) is:   Path r(t) = x(t) i + y(t) j + z(t) k   And the…

Q: Let f(r, y, 2) = e tan(r*z²). Compute fry: (r, y, z) . Simplify your final answer. %3D

A: We will find out the required value.

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A: Given:                                                                fz=x2+iy2 C is a contour…

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Q: Apply Stoke's theorem to calculate S. (x + y – 4)dx + (2x – z)dy + (y + z)dz, where C is the…

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Q: Exercise 1. * Let C be the line segment connecting 0 to ni. Then f. 1-e2zdz = a. 0 b. -0.5 + лі c.…

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Q: Let G(u, v) = (, uv). Use the Change of Variables Formula to compute the area of the image of [1, 4]…

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Q: H. GIVEN: XS = H, SR I RW, HW 1 RW, ST = HT. PROVE: T is the midpoint of RW. R W

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Q: Sketch the triangle defined by A and compute LA fdA for A = {(x, y) E R²;0< x <a and y <x} and ƒ: A…

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Q: Let B be the ball with center at the origin and radius 1 SS [3(x² + y² + z²)dV =

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Q: b) Use Gauss' theorem to evaluate f[ F· ndS where M UTM = (x² – y)i + y°z²j + (xy – y²z³)k and o is…

A: The given problem is to evaluate the given double integral using gauss divergence theorem over the…

Q: WY bisects ZXWZ and ZXYZ. Complete the proof that AWXY E AWZY. Y. W

A: Given that WY bisects ∠XWZ and ∠XYZ. We know that when a line bisects an angle, it means it divide…

Q: Show that T(u, v) = (u² – v², 2uv) maps the triangle = {(u, v) : 0 < v < u < 5} to the domain D…

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Q: soùd lines For Portions dash ùnes of borndry included in thee bmain and not include Suot1 For d)…

A: We are asked to find the domain of the function.

Q: Let : R R be different iable on R. Compute de in terms of r. y and . where y

A: Proceed as shown...

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Q: . Let C be the triangle with vertices (0,0), (2,0), (0,4) directed counter-clockwise, and let F(x,…

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Q: Let X=R2 and defined d2:  R2 x R2 to R by d2((x1, y1)) = max{|x1-x2|, |y1-y2|} Verify that d2 is a…

A: Given a function d2: R2×R2 → R, defined by d2x1,y1,x2,y2=maxx1-x2,y1-y2. To verify that d2 is a…

Q: Compute fS fdS for f(z,v, z) = 2y-z and S is the part of the cone 2-2+ betweenm z 1 and z 4.

A: Integration is the process of finding the anti-derivative function of a given function. The…

Q: Let v f(x,y) and w f(x, y). Choose a correct formula %3! to determine where J is a Jacobian. dv aw…

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Q: U tt = quna %3D u(x, o) = Cos(x) Ut (X, o) = los (2x) %3D

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Q: 7. Let E be the region in R enclosed by the cone z = Va2 + y? and the paraboloid z = a2 + y?. Then…

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Q: If f : R" →R is C' (R") is convex then f(7) > f(x) + Vf(x)"(j – x) Vĩ,jeR" | 1. Use Taylor's theorem…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Use Stoke 's Theorem to evaluate [ V. dr, where v= y²i + xyj + xzk, and c is the bounding curve of…

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Q: Integrate f(x,y,z) = (x + y +z)/ (x² +y² +z? over the path r(t) =t i+tj+3t k, 0<a<t<b.

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Q: Show that the function u = p(ry) + JFÿ¢(y/x) provides the quation „Pu = 0. dy

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Q: noose an appropriate change of variables to c al over a rectangle in the uv-plane.

A: Introduction:   The definite integral can be applied to multiple-variable functions. Consider the…

Q: Evaluate f Im(z – i)dz where C is the contour from z =1+ 2i to z z = i to z = -i.

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Q: Let B be the ball with center at the origin and radius 1 SS f6(n² + y² + z² )dV

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Q: Evaluate F. dr where C is the line segment from (6,,1) to (36, 1, and F = (sin (yz) + 1)i + (zzcos…

A: Whenever a Vector is given and we need to find line integral with two points mentioned, we first…

Q: 11. Let F(r, y) = (ry', yr') and let C be the boundary of unit square: 0 Ss 1, 0< yS1. Use Green's…

A: That's easy. Have a great day!!!

Q: let s is the curved surface of the cylinder x²÷a² + y²÷b²=1 0≤z≤c , then evaluate…

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Q: If X and Y are two independent RVs with f (x) = e*U(x) and f „(y) = e U(y) and Z = (X – Y)U (X – Y),…

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Q: Consider the surface S given by: S :r(u, v) = (uv², u + v, v³), u E [0, 1], v E [0, 2]

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Q: Let W = Span{u} where u -2. Let y = |1, find the distance from y to W L3]

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Q: B) Use Green's Theorem to evaluate F-dr, where C is the triangle with vertices (0, 0) (3,0) and (3,…

A: Explained below

Q: 17. F = |r|r, where r = xi + yj + z k, S consists of the hemisphere z = /1 – x² – y2 and the disk x?…

A: The solution are next step

Q: Find the envelope of the plane 1, C + u + a + и b + u mere u is the parameter.

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Q: which of the sets is orthvoonal under the given inner product on C[0, T] ? = S fusgıx) dx I. {1,…

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Q: Let E be the upper half of unit ball E = {x2 + y2 + z2 ≤ 1, z ≥ 0}. Compute ∫∫∫Ez dV.

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Q: Let X = {2,3, 4,..} and de fined metric on X as d (r, y) = |- yl %3D %3D Find орen ball B (2,2) =…

A: Follow the definition: B(2,2) = { x in X : d(x,2) &lt; 2 }

Q: U R Given: ZR e ZV Prove: A RST AVUT T.

A: The solution is given in the next step.

Q: Let U = R, I = { r € R | 2³ – 26a³ + 25x = 0 }, J = { x € R | |4x +2| > 10 } and K = { x € R | 2² –…

A: Note that A' means the complementary set of A. For (a), We have I=x∈ℝ| x5-26x3+25x=0. So, the…