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Q: 1. The solid that is above by the paraboloids z = 2- x² – y² and below by the paraboloids z = x? +…

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Q: Let X (2,3. 4) and de fined metrie on X as d(x, y) = |-y Find open ball B (2.2) = (0) O (2) 0 2.0…

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Q: 13 - x² – y? at (3, 2, 0), then If the point (1, 1, k) lies on the tangent plane to the paraboloid z…

A: z=13-x2-y2 Partially differentiating with respect to x, we get zx=0-2x-0=-2x Partially…

Q: The speciat sotution to the equatio %3D ho A/y)=+X B/yo)=y - %3D d/other than that

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Q: If W(-10, 4), X(-3, -1), and Y(-5, 11) dassify AWXY by its sides. Show all work to justify your…

A: Given,           If W-10, 4, X-3, -1, and Y-5, 11 of ∆WXY.

Q: Suppese That z is guen in implicit form by the equation : X°y -yz?+ X = 16 enviroment %3D in an of…

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Q: 2. Let D be the half-disc in the xy-plane given by x +y <9. 2. Calculate e-?+v}dA Select one: a.…

A: Let  D  be the half-disc  in the xy planegiven  by  x2+y2&lt;9calculate ∫∫D  e-x2+y2  dA

Q: 14. Evaluate o 4y dr + 3r dy, where C is the trapezoid with vertices (0,0), (2,0), (6, 2) and (0,…

A: The solution are next step

Q: 6. If Z is the ocentroid of AWXY, WR = 87, SY = 39, and YT 48, find each missing measure. W a) WS =…

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Q: 3, Consider Hhe following twe suctaces 2=2xy Sur 82- 5y-82=-13 a) Show that the surdaces inter sect…

A: Let the bequation of surface is given by F(x,y,z)=0 and if f is differentiable at point…

Q: 3.use Greens theorem S(1+x dx + 2xy dy ,where C is triangle With vertices (0,0),(1,0).(1,3) oriented…

A: "Since, you have asked multiple questions, we'll solve the first question for you. If you want any…

Q: Tnd he aa t the shaded egen eneloset by the talloutng tinlons 12 Set up the rleg that ge th REA f te…

A: Draw the graph and find the integral:

Q: 17. Use sphtrical coordinates. Evaluatc ||ry)dV, where E O lies betueen the spheres X'ty +Z²=1 and…

A: The relations between the cartesian and spherical coordinate system are x=rsin(θ)cos(φ),…

Q: Given, (2z – z) dz along the directed line segment from - i to 1. What is a parametric form of z(t)?…

A: We have to form a line segment from -i to 1 Let 0≤t≤1

Q: [2 Lo 2. and defined T: R² → R³,by T(X) = AX. Let A Find the images under T of u = |E|, and v =

A: Given a linear transformation T:R2→R3 by T(X)=AX where A= 2002

Q: Consider 2-dimensional hyperbolic space with metric ds ds'+dy and y > 0. The length of a line…

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Q: C Find the firet order parhal derivohve of fx,y,2). e W y-10y²23+ 43x hCs, t) =° t*In ts) + 32 4,5…

A: We want to find first order partial derivative of the given functions.

Q: Problem 52. Use Stoke's theorem to evaluate fy°dx – x³dy + z³dz where C is the trace of the cylinder…

A: Given integral and curve are,

Q: Find the orthogonal projection of y onto u 16 8. 48 OA. 32 4 OB. OC. OD. 32 - 16

A: We have to find orthogonal projection of y onto u

Q: do 10 please

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Q: Consider the cune C: (x-8)+ 4-7) When parametneing C, A tungent veotoar is i O a) r (0) = (8 +3…

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Q: Frned the poind al on 2x+y + 2' =4 n hreh bangend plana アaralle l lo tk plane x-2y +62 =5. is

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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: 1. Compute SF · dr where F(x, y) = (y²,–x²) and C is the part of th parabola u = 12 from (-1 1) to…

A: First take dot product of f and dr Then put value of y in terms of x Integrate and raise limit of…

Q: show that fGx) = C,ex +C,e* s a solution to y for all real conatanto C, +C2, and then find C,, C,…

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Q: 23 + 3 4. Evaluate the integral dz, where C is the circle (a) |z + 3| = 3, (b) |z| = 3, (c) |z| = 7.…

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Q: 1) a) far t E {0,1,2,} Comider the fa tE{0,,2,.} Conider the al fference equiim Xerg + 4Xeれ + Xt+i+…

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Q: 16. Let F(r, y, z) = ryi+azj+yzk and C be the curve of intersection between the sphere a? + y² + 2²?…

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Q: or tho gonal Use the least, me thad to find the squones projetiom of bz Ġ 2 -a anto the salwmin of…

A: Consider the given:         A=011211and  b=12-2T=12-2

Q: Show that Sa fdx + gdy = Sa - (16x*y²dx + 8yxʻdy) is independent of path: (10,5) –2) (10,5) ,-2) 4…

A: We are given a line integral as follows : ∫1, -210, 5 fdx+gdy=∫1, -210, 5 -(16x3y2dx+8yx4dy)   First…

Q: 4 6 Let y = 7 2 40 Compute the distance d from y to the plane in IR spanned by ui and uz d =

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Q: se the Divergenci Theored tobevaluhbe Sis the bSH cordinate planes whe re bounded end the planess…

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Q: of the b) nd y- Fons c) with point.

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Q: So lve the se cond order boundary Valye eF problem: Y+y+2yso where y (0) = || and y'lo)s 18

A: The given differential equation is y''+y'+2y=0......(1) with boundary conditions y0=11 and y'0=18…

Q: Given a ray r(t) = (0; 0; 0) + t(1; 0; 0), t ≥ 0, and a set of spheres of unitradius and centered…

A: Given ray is rt=0,0,0+t1,0,0, where t≥0. The given ray can be written as: rt=0,0,0+t1,0,0x,y,z=t,0,0…

Q: b) a dr+(x+yz) dy+(ry- VE) dz, C is the boundary of the part of the plane 3r+2y+z in the first…

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Q: Lee 3.1. A Usc the same at XS07=( X4 Tagler polynnencal polynimial at C=0. Dsing the algebraz…

A: To find the Taylor's polynomial of a function f(x) at , the remainder and the error, use the…

Q: Consider ф: C" — C defined by ф(x) %3D х*. a) Kerф %3D (1,-1} b) Kerø = {i,-i} %3D с) Kerф %3D (1,1}…

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Q: O 9/ Compute I - [.lryz) , uhere s is the part g the plane y +x that lies inside the half-cylinder…

A: We know that, dS=1+∂z∂x2+∂z∂y2dydx where S is the part of plane z=y+x. ∂z∂x=1∂z∂y=1 dS=1+(1)2+(1)2…

Q: 4. let f(x, y) = x² – xy + y² – y. find the direction u and Duf at Po(1,–1) for which Duf is the…

A: Given:- f(x, y) = x2 -xy+y2 -y To find:- Direction u and Du f at point p0 (1, -1) for which Du f is…

Q: n trapezoid WXYZ with bases ZY and WX, ZY = 14, YX = 10, WZ = 17, and ZD = 8.   what is the base

A: we have ; In trapezoid WXYZ with bases ZY and WX, ZY = 14, YX = 10, WZ = 17, and ZD = 8.

Q: 13-Evaluate JJI zdV E where E lies between the spheres x2 + y? + z2 = 1and x2 + y? + z? = 4 in the…

A: The given integration is , Let, I=∫∫∫EzdV change the integral into spherical coordinates Put x=r…

Q: 3.2. let f(x) = 2, x+4 xez, * 1 - 1 1/2/20 -74x45 -*>$ Approximate the foldoy using Trapezoid mule…

A: In order to approximate the integral: ∫abydx, the trapezoidal rule uses the formula:…

Q: Complex Analysis

A: For given function, First we will show the function is harmonic function as shown below :From the…

Q: In AFGH, M is the centroid. If FM=20 find FK. G J K F H L

A: Given: In △FGH,  M is the centroid of the triangle. FM = 20

Q: Ex.5 Given the Jordan curve y that is the counterclockwise oriented boundary of the set T= {z=x+iy :…

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Q: 3.use Greens theorem s (1+x5 dx + 2xy dy ,where C is triangle With vertices (0,0),(1,0),(1,3)…

A: Apply greens theorem

Q: if Vx 1 dA if R is the unit circular disk. Find Lütfen birini seçin: O A. 3r(22-1) O B. 27(/2-1) OC…

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Q: Save and Exit Question 18 Which statement is sufficient evidence that A LGE A AMR? R O A) ZL E LA,…

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Q: 2) The double integnal | 3x ekdy, whetzeT is the tniang le of VErtices 6,0),c2,0) ond (eti-2),…

A: The double integral is an integral with respect to two different variables the integral of a…