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Q: he geneCral solutION UI tind the pacticular soluetion of the di fforentral equatkoK 24-20 givon y=3,…

A: We have to find Perticular Solution for given differential equation using y=3, x=2.

Q: Find the domain and range of:

A: (a) We know that the domain of the square root function is always greater than equal to 0. Thus,…

Q: Solve the initial valwe problem using Laploce trensformotion. y (4) + 2y'(+) +5y(+) = esint y lo)-0…

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Q: if z=xarctan(y/z), find ∂z/∂x at x=0, y=1, z=1

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Q: Syy-mat sama dy ³

A: Follow the procedure given below.

Q: Given: YX - XZ, WX bisects ZYXZ prove: AWYX = AWZX

A: Given: Prove:

Q: if y = secx prove that y^2+y=2y^3

A: Equation relates the number of variables combined together by algebraic entities using equality…

Q: If f(u, v, w) is differentiable and u = x - y, v = y - z, and w = z – x, show that fe af af + = 0.…

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Q: Compute ff, x²ydA,where Dis the triangle bounded by x = 2, y = 1, y = 1 –

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Q: Let -2xy – 3yz – cz, x = st, y= e", z=t? Compute ди (4,-5) = ds dw (4,-5) =

A: The given function.

Q: 12. Calculate the area and volume of a sphere knowing that the length of its equator is L = 12p cm.

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Q: Solve min udr, subject to u(0) = 0, u(1) = 1, ur'dr = c %3D =C.

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Q: If X = U+v , y =U-V then Show that + 2 du? = 2) ( %3D nene Than ded uce that wok cu+ v*+ (u+v) g…

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Q: If x,+iy,=x,+iy2 then x=y, %3D

A: TRUE for part (1) It is given that x1+iy1=x2+iy2. x1+iy1 and x2+iy2 are complex numbers Two complex…

Q: dy let y = xtan z then is da elect

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Q: If z = In /x? + y? , find x- X +y В. 1 С. D. Vx? + y? A.

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Q: : Scot y dy

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Q: Ql if (x,y,z) =o and Z"=x+Y find d2 (using di f Beren tials concept)

A: Given  If f(x,y,z) = 0 and z2 = x + y

Q: Let X and Y be iid N(1,3). Let U = 4X + Y and V V_dependent or independent? Justify your answer. 2X…

A: Given X  and Y be iid with N(1,3). Mean, μ=1 Standard deviation, σ=3  U = 4X + Y and V = 2X — 3Y

Q: Compute |// a² d.x dy dz, where E = {(x, y, 2) : x² + y? < 1,0 < z < 1}.

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Q: af (2,0) ay f(x, y) 3D хетУ + 5у%; af (2, 0) = Əy

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Q: What is the dimension of {(x, y, z) E R³ : x +y+z = 0}?

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Q: A If w= f (x, y), where x = rcos 0 and y = rsin 0 , show that 2 1 + 2 +

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Q: Solve Ut = Urx, x > 0, t> 0, u (x, 0) = f (x), u (0, t) = 0.

A: Given partial differential equation isut=uxx,     x&gt;0,     t&gt;0ux, 0=fxu0, t=0

Q: 9. If y = V-|x|, then Dr = %3D %3D

A: Df :  Domain of function f  The set of all input values where f defined

Q: 23 { , si (x, y) # (0,0) b) g(x, y) = 2x2 + y² , si (x, y) = (0, 0)

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Q: (1,1) S[3x*+5y+i(x°-y°)] dz along y=x Evaluate (0,0)

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Q: If & = {(z, y, z) | 1< * < 2, z < y < 2a, 0 < z < z +2y} then: SI. 3zz dV ニ

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Q: O Civen w (2-31, XL-4,9),Y(S,y) and z(-1,1) find the Value so that ux LYZ

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Q: If i = xi+yi+zk then grad (r") is equal to

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Q: 3. Assume that z= 2(r.y) and ee = ryz Find and

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Q: Find Duf at P. 2 f(x, y, z) = 6x³y°z°; P(2, – 2, 2); u = ;i + -k

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Q: Solve Utt currrx = 0, -0 0, %3D u (x,0) = f (x), Ut (x,0) = 0, -0 < x < ∞ ||

A: Given that,utt+c2uxxxx=0-∞&lt;x&lt;∞t&gt;0ux, 0=fxutx, 0=0The pde is solved as shown below

Q: If ø(x, y, z) = ry²z find grad ø at (2, – 1, 3).

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Q: Q- show that yo+(?) sy + (2) B²y_₁ = y + (1) DY...+ (1²¹) Ay -

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Q: 2 2xy) dy, v es (0, 0), (2, 0), (

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Q: - Calculate the 2D 32×32 DFT of ƒ(r,y) = 26(r,y)+ 6(x – 15, y – 16).

A: The given function is f(x,y)=2δ(x,y)+δ(x-15,y-16) The 2D DFT signal is given by…

Q: (b) ƒ(x, y) = Vy – x · In (y+x) -

A: Given (b) f(x,y)=y-x ln (y+x)

Q: Find the discontinnity point of &Cz): ニ そzそ+

A: Given that, the function is fz=z+1z2+2z+1. Set z2+2z+1=0 to find the undefined points. Compare the…

Q: O, x = 2, y = dy dz is

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Q: BeR NOULLI 's EQUOTION (2yーX)d水+ラ×ydy:o ソ+PCx)yq(x) yh XrlwDepenとn 3 y= Depen Dest

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Q: O Find tor foaunctric yuatrn yzl+2tan o, 1: 2rseco

A: y=1+2tan∅x=2+sec∅find d2yd∅2 Since multiple questions are asked, according to guidelines, I am…

Q: GIVEN WX= VZ, WY = VY, YZ = YX PROVE ► AVWX= AWVZ %23 十 %23 Plan: What do I know? What do I need to…

A: Solution: The objective is to show that the given traingles are congruent

Q: xlet X,Y,7 be v.V.J with Joint fA くれく くらくtyerzc

A: The joint probability density function is given to us the conditions on x, y, z are also given to…

Q: where: %3D Solue ulX, o)=2 X •a u (0,t)=o 1 ノ

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Q: 11T |13T V2 - V6, determine the value of sec 60. Given that sec 12 %3D 12

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Q: Using Eirjenvelue melthed envalie methed +2y dy ?a-2y 3 of

A: Given that, dxdt=-52x+2y   and dydt=34x-2y write in matrix form, x'y'=-52234-2xy for eigen values,…

Q: Prove the identity by manipulating both sides.

A: Take L.H.S. and solve

Q: 2. Given z = , show that ху xy(zxx + Zyy) 2 y - x3 x²y? |

A: Function is the unique relation where each x is mapped to unique y. It can be of many type,…

Q: l? sc tue suell metuozd to fired tue voune of te Solid genented the by rerolning the plene rgim…

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