3)- find ahe pr patikular solustien of theditfrential equatisnx+Cx =CL given the x6)=a Ax 20 at t=o where LikGmy- d't all are Gnstants-

Q: 1. Use an antiderivative to show that for every contour C extending from a point z₁ to a point 22, 1…

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Q: 6. Evaluate (7xi - zk) · ndA over the sphere S : x² + y² + z² = 4 (u) by the Divergence Theorem, (b)…

A: The divergence theorem states that  ∬SF·ndA=∭V∇·FdV Where, F is the vector field, V is the given…

Q: E valugte the cube raot of z when 2=27 Cis(210) ( Let 0s GS360°) Smallost ☺ ualus) targonst ualue).

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: The value of the triple integral 6zdV where E is the upper half E of the sphere of x² + y? + z? = 1…

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Q: Ex: © Suppise that the fiowing Aransferuntin Conneclğs the lei) and (ti) coordnate Syshems; a4ス?) 2…

A: Given that, ζ=x¯1=ex1+x2x¯2=ex1-x2 To find: a) Jacobian matrix J and J-1 b) Compute J¯

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

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Q: L'équation 423 = In (e4% + 2ay) définit implicitement z comme fonction de x et de y au voisinage du…

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A: Consider the given path rt = cost , cos2t , sint  Then, xt=cost , yt=cos2t , zt=sint

Q: 5. Verify that the. functrun.u=1/ xy2? satis fies the threendimensianal.place cop.x+Uyy.+Uzz =o %3!…

A: Rrrrrrrl

Q: 5. Conclude on the limit of f(x, y) = +v4 xy2 as (x, y) → (0,0) along paths y = mx and x = y?

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Q: Prove thut:f focK, 2) Y is a contimans findion then, g=XxX-> YxY 3 3 n K2) = (F(), PU=) Einction is…

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Q: find the Lineartransfromation T:Manz (R)R whose matrit Mp --

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Q: The dispiacement tunchon of Object A is S,(t) =t 3-2t²+4; and the cispiacement funchon of Object Bis…

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Q: b) Show that the implicit Trapezoidal method h Wi+1 = Wi +5 f (ti+1, Wi+1) + f(ti, w;), is…

A: The solution is given below in the next step:

Q: Find to the the equation du green funclion corresponding pula)=fex) conditions U(o) =0 with and…

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Q: 22. Compute the contour integral (Баллов: 2) Sof (2) dz, z E C, if f (z) = and path is semicircle z…

A: Topic:- application of integration

Q: Solve using horizantal Slide EX Evaluat..f.x.dA.whak.R.a.the.sgen.in.the figt.…

A: ∫∫R f(x,y) dA= ∫∫R f(x,y) dxdy =∫∫R f(x,y) dydx

Q: Cannot solve

A: Multiplying and dividing first term by secx and second term by tanx of left hand side of equation ,…

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A: It is given that on considering that let X,Y,T be the distinct points The objective is to show that…

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A: See answer below.

Q: t in 30 minute please duopoly with homogeneous goods. There ar

A: When there are only two firms in the industry, it is in their advantage to collude and set the price…

Q: How would I solve ∭xzdV, where E is bounded by the planes z = 0, z=y, and the cylinder x2 + y2 = 1…

A: Solution is given below:

Q: Compute (ax + by² + cz) dS over the sphere x +y +z² = 1.

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Q: 4. Prove that fer*dr+xydy = f, So*(y– 0)dydr where C is the triangular curve consisting of the line…

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Q: IF en Inner pYoduct Space X iS Vea show thet condition Hnll=Hyll impLies +ye X-y>0c what does this…

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Q: Qs Findl the Fauier Ex pensian of Hhe funckian deld in a gula Parul by the weladons Sule Perial by…

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A: This is a problem of line integral. Since the path given for line integral is embedded on the x…

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A: Given.The differential equation is

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: consider the curue desoribed by 2y"-x²_4y vevity that the foint (4-25 les on this o8 wrE andd find…

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Q: . Show that the function u = p(ry) + Vry v(y/x) provides the quation = 0. ду? %3D dx²

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Q: Sketch the solid described by the given inequalities. 0srs 8, -T/2 se S T/2, 0szs 1. 1.0 1.0 z05…

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Q: Jraen fusk hon conespaaday to o d'u z ul) = flx). dx² Find the the egualido for conespoodiang to…

A: Given differential equation is d2udx2+u(x)=f(x)                   (1) boundary conditions are…

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A: Given that the integral,

Q: 8. Evaluate the double integral // ydrdy where T is the triangle with vertices (0,-1), (0,5), (4,…

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Q: Supose z is implicitly defined by the eq qy+ 3x*+ XyZ + 3Z=9 in an emvoment of the point P(0,3) in…

A: In this question we will use basic of vector calculus i.e concept of directional derivative. We will…

Q: Evaluate the line integral §. xy²dx + 2x²y dy over triangular path with vertices (0,0), (2,2) and…

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Q: Evaluate the line integral x²z ds, where C is the line segment from (0,6, 2) to (8, 5, 1).

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Q: 13 ABCD is a trapecium with ABDC. A line parallel to AC intersects AB at X at Y Prove that ar…

A: Since you have asked multiple question, As per our policy we will solve the first question for you.…

Q: Thelem:-TP PTR har ociva bveof %eI,theu f is Coutivlalse- at Xo CTs thecouvese of thevem triue?why?

A: Questions from continuity and differentiability

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: ) Use the eisenfunctan expausian melbud Solve the vibrating strng Problem = 4 uxx + Sin zx…

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Q: let A and B be matiices of Con det A) = -1 find the Valué of Cdet(z AT) - dct(-2B )) LA Pproxi mate…

A: Given:- det(A) =-1/2   ,  det(B) =2/3 To find:- [det(AT/5) -det(-2B-1)]2

Q: Ex: © Suppise that the fuowing trausfruntiun Cowneciğa the (I') and (xi) coarduate رک سهاور؟ てス4ス)…

A: Given  x¯1=ex1+x2x¯2=ex1-x2 Required Jacobian is…

Q: Evaluate the line integral ∫Cx^3z ds, where C is the line segment from (0,3,8) to (8,4,6).

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Q: => For The Wbech Ualuo of E doas the Martrix イK %3D have one roal eaomalue of Mutiplicty?? k =

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Q: D.Prove that y y(2)= U12,9)+ jve (2,4) anelyli the loplale's as z, than Guetion u and v Satiglics

A: Consider an analytic function f(z) of the form . Then f(z) will satisfy the Cauchy-Reimann equation…

Q: THE DiffieRENITAL ECLATDOM WITH INITIAL conoirDON. dy- XSENX こ dx 3.2

A: Given query is to find the solution of the differential equation.