b)Show that, 6(z, 3zy – y' and (z,y) = -+3ry are harmonie

Q: 4. Show that z = a' Zax if z = e-al cos(x-at) %3D

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Q: 5. Prove that So*(y – 0)dydr =

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Q: Find 3²y of z = In(xy)

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Q: If =x+3y-z,=4xyz, w=22 -xy evabuate d(u, v,w)/ (, 2). at (1-,0).

A: We have to first find all partial derivatives.

Q: az az and at the point (-1, -3, -2). Suppose ry z - 94 = 4xy – z. Compute ду dz |(-1,–3,–2) az…

A: An important result from advanced calculus, called the Implicit Function Theorem,states the…

Q: Construct a clamped cubic spline passing through the points 9, 13 and 22 with fx=x3+1

A: f(x)=x3+1y0=f(9)=730y1=f(13)=2198y2=f(22)=10649 Here h0=4h1=9 For given set of points (x, y) that is…

Q: XYZ is given with X(2, 0), Y(0, −2), and Z(−1, 1).  Which of the following can be used to prove that…

A: The answer is given as follows :

Q: 1 dæ using the residue theorem. (2² + 1)° Evaluate the improper intergal -00

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Q: Q1. Verify Euler's theorem for the homogeneous funetion, fxy.2)-axy +byz + czu

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Q: xy If z show that: x- y

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Q: 3. Solve for the Z-Transforms and ROCs of: x[n] = [6, -2,2,0,0,4, -3]

A: We have to solve the given problem.

Q: 2)Give of a homogeneous syatem of equatians with 2 equations and 2 unknoan's. 3), Why is cury…

A: 2) Take the system of homogeneous equations            x+y=0          x+2y=0

Q: 1 Using Convolution theorem, find L' ,2 |(s² +a²)?

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Q: Find дхду of z = In(x² – y) %3D

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Suppose that (Q x Q, +,.) is a ficld where (x, y) + (z,w) (x+z,y + w) and (x, y). (z, w) (xz +2yw,…

A: I have find identity of the field and then inverse

Q: 6. Use a substitution to find S (x* + 1)" z³dx.

A: Here we use substitution we find∫x4+111x3dxHere we substitute x4+1=du…

Q: (b) Compute r if: arctan r + arctan 1 = 2 ( arctan z arctan

A: tan-1x+tan-11=2tan-1x-tan-113

Q: Find y,(x) if y = In(In(Inx)).

A:

Q: A fence is to enclose a rectangular possible from with area of 400 square meters if P(x) is the…

A:

Q: Verify Young's Theorem z = In(2x + y) -

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Q: (2) Suppose that G, C Zn-r. Then prove that G,-1C Zn-r+1

A: We prove that

Q: Show that if AT Ay = y for all y in Rn , then ATA = In .

A: Given that     ATAy=y  ∀y∈Rn. To prove ATA=In

Q: Verify that (AB)" = BT AT %3D التحق ق 3 2 4 2 1 3 A = 2 1 B =1 2 5 4 2 3 0 2 1

A:

Q: az Find if yz – In z = x + y ax

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Q: 3. For Z = x²secy,prove that Zxy is equal toZyx

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Q: If C, C2 Cn are Constovts 1-1 . a,, uzXz) ---- Un (X)ave livffen antiable 4111 funetions at x with…

A: Introduction: The differentiation of a function y=fx is defined as f'x=limh→∞fx+h-fxh This is…

Q: Show that the Adam-Bashforth method 3 Yn+2 = Yn+1+hf(tn+1,Yn+ 1) – hf(tn,Un) has local truncation…

A: We have to show that the Adam-Bashforth method            yn+2=yn+1+32hftn+1, yn+1-12hftn, yn…

Q: 0, 2 is defined by A natural cubic spline S on 5. So()12x - 0 if 1 (1) S(r)2b(x1)c(x - 1)2d(x - 1)…

A: 5.Note that, the natural cubic spline must satisfy the conditions

Q: Let æ² + y² + z² = 3xyz, th = 3ryz, th

A: Given that, x2 + y2 + z2 = 3xyz We have to find (del z)/(del x).

Q: Find дхду of z = In(x² – y)

A:

Q: prove that esch'x - In (* + x2 %3D

A:

Q: let z- 5 dy By chain Ruie

A: Given z = √x dy/dx = (1/2√x)•(dy/dz) We have to find d2y/dx2 .

Q: 16) 1. ZDX 2. -X Show Your Work Valid Invalid

A: We have: Z⊃X~X ∴~Z    This can be written as Z⊃X∧~X⊃~Z  Here, p⊃q means "if p then q" This argument…

Q: Find the linearization of y = ev7x at x = 16. (Use symbolic notation and fractions where needed.)

A:

Q: b) Verify uxy = Uyx , if u = In /x² + y² . %3D %3D

A: Consider the given function. u=lnx2+y2 To verify the equation, find the derivative first with…

Q: Expand xy² + 2x – 3y in powers of (x + 2) and (y – 1) upto third degree | terms.

A: Given ,  f(x,y) = xy2 + 2x - 3y  By Taylor's theorem  f(x,y) = f(a,b) + {(x-a)fx(a,b) +…

Q: 2.) Use the chain cule to find dz and d ond guen the fllowng: Yoy must show in work that your the…

A: We have to find partial derivatives.  Concept:

Q: Find the Reat teng th of sides of the triungle (AB Al4, 6,0), BL-6, 2,5) yclo, 9,5 ).

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Q: Verify Eular's Theorem for z=ax²+2hxy+by2

A: According to Euler theorem,  x∂z∂x+y∂z∂y=nz Where n is the degree of the homogeneous equation.

Q: 8-JIE FCx²_ ye, y-z²) =• then Prove that + Xそ 2Z

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Q: true or false without justify The sel { 1,2,t, 3,,4,+, csx, coss is mot Ti Bomded in (CToi], Ul6)…

A: True.

Q: 1. bility and find the cofact +22=1 %3D - = Z to waishs buing

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Q: 3. Show that à = (6xy + z³)î + (3x² – z)ĵ + (3xz2 – y)k is irrotational. Find p such that A Vọ.

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Q: 8. Use the Chain Rule to find az/as and az/at. z = (y-2x)³, x = s³t², y=s+t²

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Q: Find y' in y = (x³ 3x²(x²+e) x³ +3 A. y' = B. y' = C. y' = +3)(x²+e) +7x6 In (2³ + 3) +7x6 (x³ + 3)…

A: Understanding of derivative when function is there in power of any function.

Q: If C, Cz - Cn are Constovts 2111 . u,), uzX2) ---- Un (X)ave Livffen antiable 4111 funetions at x…

A: Introduction: Differentiation is a property of a real-valued function. When the independent variable…

Q: Find leng th of the Cardioid Vsa6 from e -oto0 - 1 %3D

A: Use the formula of the length of the polar curve. L=∫0πr2+drdθ2dθ Here, r=aθ3 and drdθ=ddθ(aθ3)=3aθ2…

Q: Show a complete soluton 2 3 CO-10y 10sin x

A: Given:

Q: Show that lm Casy -1 CoSy-1

A: