for w = x sin y +y sin x + xy. W yx Q2) A) Verify that wry

Q: Show that if sin z| is bounded along the straight line {(x, y): ax - By = 0}, then a = 0, i.e., z…

A: In this question, we have to prove z is in real R.  here we use the property of the hyperbolic…

Q: Let /:R'R. S(x. y.2) = (e' tan y,x' In y). Compute D(f).

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Q: Show that the function u e(xy) + Vry V(y/x) provides the quation = 0. dy?

A: Again differentiate,

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: Show tuat a fuinchon fiR?>Rlefined by 3ں۔x5 ,ie (xxy]#Cojo) f cary)e je xcy=o Is continuous at (o,e)

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Q: Use Green's theorem to evaluate Sc(y² + x³) dx +xª dy where C is the perimeter of the square [0, 1]…

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Q: 20. Show that a²F(x, y) -dx dy дх ду over the rectangle xo < x < x1, Yo < y < y1, is F(x, у) — F(x0.…

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Q: evaluate by Sto ke's theorom Gcyzdx+ zx dy+ xydz),where Cis the Corve xày=1, z=y: [ Hint: §…

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Q: Let z = e* sin(y+a), show that %3D ôx? oy?

A: Given, z=e-xsiny+a, then we have to show that ∂2z∂x2+∂2z∂y2=0.

Q: Given that F(x, y, z)=sin xi+ cos yj + xzk. Evaluate ſ. F.dr where C is given by r(t)=( r', –f,t) ;…

A: Given that

Q: Determine la derivada direccional de f (x, y) = y In z en el punto P (1, 4) en la dirección de v = i…

A: Topic:- calculus

Q: Prove that A <m AUB where AUB = {0x | r E A}U{ly|y € B}.

A: Solution: Let us consider two sets A and B. It may be possible that A∩B≠∅. But we want to construct…

Q: 4. Which would not be sufficient to prove AWXZ AWYX? C ZWXZ = LY WZ А WX XW YW WZ D WX WX XY XZ WX…

A: To show that the given two triangles are similar we need to show that the sides of the two triangles…

Q: If u = x°f(x/y) according to Euler's theorem xUx + yuy is 5u %3D

A: given that u=x5fxy verify whether xux+yuy=5u is true or false

Q: Suppose that u = Va2 – y? and v = arcsin() where x-y 0 and- . Which of the following is/are true? A.…

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Q: Complete the following proof. Given: XY 1YR, RS 1 YR XY Prove: SR YZ Y. R. RZ Because XY 1 YR, RS…

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Q: If z=sin(x^2+y^2),x=vcos(u),y=vsin(u) find ∂z/∂u and ∂z/∂v.   ∂z/∂u= ∂z/∂v=

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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: 7 Prove : id Is perpendicular line to ra duic at its outer end point ,then t ang ent to the cirde is

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Q: Let x,(t)-v(t)+sin(r), x,-vt) then x,(t)= xN-cosit) Select ones True, False

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Q: find ow/ar if w = (x + y + z)², ar www w x = r – s, y = cos(r + s), z = sin(r + s) at the point (r,…

A: See the attachment

Q: Let 0 be the angle between the line y = mx +band the x-axis. Prove thatm = tan 0.

A: The question should be :                 Let θ be the angle between the line y=mx+ b and the x-axis…

Q: a²f If f(x,y) = e" sin (r + y), then prove that дхду дудх %3D

A: Hi! You have posted two non-related subparts. As nothing is specified, we are answering only the…

Q: 2 Evaluate the fullowng cartesianntegrat changing theminte equivalent Pelarintegrals: Fー dxdy 2-

A: We have to find the double integral using polar coordinates.

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

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Q: that ulx,y) = 42 Cos 3y is the particulas -3X prove Solution of Uxx+Uyy =0 u cx, 플) =0 where…

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Q: Given: ZW and ZY are right angles WX = XY Prove: AXWZ EAXYZ

A: GIVEN:- LW=LY=90 WX=XY

Q: Compute where h(s) = rs? -r. Assume r is a constant. %3D ds

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Find up +Uy given that u (x,Y)s. (x,x)s

A: Given that ux, y=tanx3+mx2y2+my4m-x2-y2 To find ux+uy we follow the following steps calculate…

Q: Find aw in terms u and v if du w= In(x2+y2 +z²), x = ue" sin u, y = ue' cos u, z = ue"; (u, v) =…

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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: If the region R is bounded between two circles x² + y = 4, x² + y = 9, then we have: sin(Vx2 + y?)…

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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: Let F(x,y,z) = z* + x+ y sin x + x In z 0, where z fx.y), then at (0,0,1) and are dy equal to: ax

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Q: Prove that (x+) ) is the rolution on the dipporen tial equation y'+ y-e 9= C,e*+ C2x + Cg, y" - 4 y"…

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Q: O Given the initicl bouridary conditions y(0) =0, y'c0) = 1, letrmine the, solntiem of %3D…

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Q: Show that the function u = p(xy) + Vry v(y/x) provides the quation = 0. dy?

A:

Q: 2. Which of the following statements is TRUE about rectangle WXYZ. X z, 10 Figure 1 WV = VZ XZ XY O…

A: Given query is to find correct statements for the rectangle WXYZ.

Q: Use Green's theorem to evaluate s cy? oy)dx + (y²rlo4") dy where Cis s hoon belbw, N y = 2-x² G,1)

A: The given path contains 4 curves: C1:  from (1, 1)  to  (-1, 1)C2:  from (-1, 1)  to  (-1, -2)C3:…

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: Solve the problem with Neumann oundary conditions, - Uxx = 0, x, t > 0 u(x, 0) = f(x) ux (0, t) = 0…

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Q: Prove that 3x +8 Viv = dr dy: %3D where R [-1,1] x [0, 2).

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Q: If f(z) = sin(z 2) = U(x, y) + iV (x, y), determine U and V . Verify that the C-R conditions are met…

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Q: Show that if |sin z| is bounded along the straight line {(x, y) : ax - By = 0}, then a = 0, i.e.,…

A: We know, sin z = sin x cosh y + i cos x sinh y, Where, cosh and sinh are hyperbolic functions.

Q: (R, d), where d(r, y) = |r – y|, is separable. %3D

A:

Q: Qz: IF U=h cx,g )= Lnce+ ě).show that %3D Sy

A: