Se t S: 9 メ ;メENI a-) Find the supremum & infimum and prove that it is bounded above and below. 6) Is the extre ma found in S

Q: H.W where r is the selid bounded by the Sur faces

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Q: Let Wbe the region bounded by z = 4 – y?, y = x², z = 0. Compute fw x + y+ zdV.

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Q: 5xcos(y)dA, D is bounded by y=0, y=x2 ,x=9

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Q: Use Green's Theorem to evaluate | F nds, where F = (Va+ 5y, 4x + 5y) %3D C is the boundary of the…

A: We have to evaluate the integral ∫CF→·n→ds, where F→=x+5y,4x+5y. Where C is the boundary of the…

Q: Evaluate the double integral. / 4x2sin y²dA; R is the region that is bounded by y = x³, y = -x³, and…

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Q: Let R be the region bounded by y = 5 sin(x , y = 5(x – 2)²,

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Q: nclude spaces in between 5. d te In (In y)) at y dy

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Q: /Evaluate The are bounded by The Semiellipes y =2J5-x' oP The line 6 X = ±1 ,Y=-1 %3D

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Q: Consider the solid that is bounded above by x² + y? + z? = 169 and below by z=5. %3D

A: In this question, we have to write the triple integral to find the volume of the solid bounded by…

Q: Use Green's Theorem to evaluate: F dr x² and the where F = (Va +6y, 4x + 6y) and C is the boundary…

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Q: Evaluate using Green's Theorem ф худх + (х + уjdy Where C is the boundary of the region between x? +…

A: From Green's theorem:   ∮F1dx+F2dy=∬∂F2∂x-∂F1∂ydxdy   Given:   I=∮xydx+x+ydy   F1=xy⇒∂F1∂y=∂…

Q: 4. Finl the volume bounded by the surfaces z x2 and z 4-x2-y2.

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Q: Let C:z|=1 in the counterclockwise direction and I = $. dz, J = f. Lnzdz, and K = $. tanzdz. For…

A: We can apply cauchy Goursat theorem on I and K but not on J

Q: Use Green's Theorem to evaluate n ds, where F = (Va + 5y, 4x + 5y) and C is the boundary of the…

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Q: Set up, in either Cartesia over the region within the cylinder x² + y² evaluate the integral. 2م

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Q: a) F(x,y, z) : planes x = 0, x = 1, y = 0, y = 1, z = 0, and z = 1. 3xi + xyj + 2xzk and E is the…

A: Solution of (a) is in given below

Q: 3- calculate SSm xe' dxdy -if the bounded set M is given by inequalities y <2 - x, y 2 x². -Draw the…

A: The region y≤2-x isThe region y≥x2  is The region M is,

Q: Let S be the collection of points (x, y, z) that satisfies all of the following inequalities: 0 ≤ x…

A: Here Z is function of x and y so first we have to integrate w.r.t z then x and y.

Q: H.W Ennlunte where o is the selid bounded by the Sur faces xサ 0 7 そー

A: Given term is: ∫∫∫Sx2+y2dzdydx and the surfaces are x2+y2=z2, z=0,z=1

Q: garded as a subset of R. 9.E. y ing theargme ang ), prove that the interval J = { (x, y) : 0 < x <…

A: 9.F  We have given J=(x,y):0≤x≤1,0≤y≤1   to prove the compact in R2 we have to show that J is closed…

Q: Evaluate y xz dV, where Wis the domain bounded by the elliptic cylinder = 1 and the sphere x? + y +…

A: We need to evaluate ∭Wxz dV, where W is the domain bounded by the elliptic cylinder x29+y216=1 and…

Q: Evaluate the triple integral edV where E is bounded by the parabolic cylinder z = 1 - y² and the…

A: Given ∭x8ey dV

Q: Let I = , zdV ,where D is bounded by the planes x = 0, z = 0, x+ y = 2 and the cylinder x2 + z2 = 1…

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Q: SI xyz dW, B is region bounded by two cylinders, wwwm w В x^2 + y^2 = 16, x^2 + z^2 = 16, and the…

A: Consider the given volume of the two intersecting cylinders given by  x2+y2=16 andx2+z2=16  as shown…

Q: Ry (T) is bounded by its value at the origin i.e., IR, XX XX (T)l<Rxx (0) XX

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Q: t BLX,X) denoted set f al incod bounded operates an defined on ow hat fex every TE BLXX) for Hhe…

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Q: 5 Compute the Surface area f obtained by revoluing the line y=x around the y-aris. a cone whichü

A: To find the surface area of cone which is obtained by revolving y=x revolved around y-axis.

Q: and y have density flay)=82y tor Find ECX14) and ECYIX) リフズ7679 %3D

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Q: As the region E is the region bounded by y=x2 , x=y2 , z=0 , z=x+y,  Calculate the triple integral.

A: It is volume integral

Q: 3. Evaluate JS Vr2 + ydA, where R is the region bounded by the circles with center (0,0) and radius…

A: (3) Hello. Since your question has multiple parts, we will solve the first part for you. If you want…

Q: as Find Hhe voleime of odid generated by revolving tthe region bounded by graphs of y=xe;y 0, and…

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Q: Consider the region D in the xy-plane which is bounded by the following 2 -, Y = 4 y? = x and y' =…

A: Evaluate the integral in two ways. Directly and changing the variables. Last image is the shorter…

Q: Find the volume of the 'ice-cream' that is bounded by x2 + y2 + z2 = 77 and the upper cone z2 = 3x2…

A: We have to find the volume of the 'ice -cream' that is bounded by the sphere  x2+y2+z2 = 77 and the…

Q: evaluate the arca of He reginn bounded below by and y= aboue by y=X

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Q: Sketch the region which is defined by the given condtions. 0 ≤ θ ≤ π, r ≤ 3

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Q: 4. Evaluate f, 2ry dA, where R is the region bounded by y i and

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Q: /Evaluate The are bounded by The Semiellipes y=25-x' oP The lines X = ±1,Y=-1

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Q: Sketch the bounded region enclosed by 2y = 4/x, y = 3, and 2y + 3x = 7, then %3D find its area.

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Q: Find the volume of ane hal f cylindder that is bounded 5 above by the Plane z= 4. belowe by x -y…

A: According to give, We can conclude from the diagram that the half cylinder has  1.height in positive…

Q: Use the Cauchy integral formulas to evaluate the eiz cos z dz, 2²(2z – 37) where C is the region…

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Q: Let C be a simple closed curve bounding a region Din R2. which of the following are equal to the…

A: Let C be a simple closed curve bounding the region D in R2.  So using Green's-Theorem,

Q: Calculate the line integral F-dr where F(r, y) = (x – y³, y + r³) and C is is the circumference of…

A: Given function is F(x,y)=&lt;x-y3,y+x3&gt;=x-y3i+y+x3j=F1+F2(let)Where F1= x-y3 and F2=y+x3According…

Q: Compute s F=

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Q: he volume bounded by y = x², y = 0 and x = 2 rotated about the specified = specified orientation of…

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Q: Q4: State the Fundamental Theorem of Independent of Path and Morera's Theorem. Why can't apply these…

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Q: Evaluate the double integral ∬DxcosydA,∬Dxcos⁡ydA, where DD is bounded by y=0,y=0, y=x2,y=x2, and…

A: To evaluate the below double integral Here D is the region bounded by y = 0, y = x2, and x = 4.

Q: Let D be the portion of z = 2x + 5y inside z? + y? = 1, oriented up, and let %3D F (y, z, –2).…

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Q: Let C:zl-1 in the counterelockwise direction and I = 4, Lnzdz, J = , ždz, and K - $, tanzdz. For…

A: Last optiom is correct  That for only k we can apply cauchy goursat theorem

Q: Prave by indretion ŽKczkt) z on n that for all integens aoenzl, 2.

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Q: he region bounded by the cylinder x2 + y2 = 9 and the planes z=0 and x +z =9 O 243 O 81T 27TT 729TT

A: Follow next step