-5-S"S, ((m-3)x²+m(m -! x- Yy)-4myx] dydx 2,3m

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

A:

Q: The Critial Points of fcx,y)t+Ý-4y subject to the x+y=9 is O (o,さ3), (は5,2) ④ (e, さ)さ何,) None of…

A:

Q: 1- iz If z = x +iy and w =- z-i show that w = 1= zis purely real

A: Use modulus property

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

Q: 5.Use thelefinition to Rrave that Jw wh- 2

A:

Q: Evaluate / (x - 2y + z) ds. S: z = 3 - x, 0sxs 3, 0sys 2

A:

Q: Suppose that Mrs. Jena (in the position of T) want to travel to the top of regions diagonally right…

A: To find the number of route to reach the top of the region :-

Q: A natural cubic spline is defined by Sa,(x-1)' +b,(x-1)² +c, (x - 1) + d, S(x) =- if 0sxs1 (x- 1)' +…

A: Step:-1 Since, we know for cubic spline S(x)=S0x=a0x3+b0x2+c0x3+d0…

Q: Find yas a fon chenof x if t. %3D with

A: This is cauchy euler equation and we will solve it by changing the dependent variable

Q: ) If ƒ(x,y) = 3x²y + cosy+ ysinx – e2x then verify fxy = fyx

A: fx and fy are the partial deferential of function w.r.t x and y respectively. Then fxy is the…

Q: Let Z, = 2 cis 30° Z2 = 3elli %3D Z = In (1 + i) If Z = Z,Z, +Z3 Find IZ.

A: First we convert all expression into a+ib form then make necessary calculation.

Q: Use chain rule to find az at (u, v) = (1, 1) if

A:

Q: Which elements are invertible in Z4[x,y]?

A: W need to find elements which are invertible inZ4x,y.

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A: A joint probability distribution gives the probability for two variables together which is…

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A:

Q: dz Let z-ay" – 4r, * = uv and y-v - 3u. Compute Ən (u,r)-(1,1) -

A:

Q: 4Ux+Uy=U² , U(x,0)=1/1+x²

A: In the given partial differential equation with the given initial condition. 4ux+uy=u2u(x,0)=11+x2

Q: Compute ∇ƒ(-1, 2, 1), where ƒ(x, y, z) = xy/z.

A: Given,f(x,y,z)=xyz     As we know ∇f(x,y,z)=∂f∂x,∂f∂y,∂f∂z

Q: To/t Integrate Ua ko To 3. Uz kg 2. eT-1

A:

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

A:

Q: 4: verify that wy = Wyx . ریاضيات المرحلة الثانية a w = In (2r + 3y) %3D

A:

Q: 1. For U, iid uniform on (-0,0) show that - min, {U,} is sufficient for e > 0.

A: # given ui follow  uniform distribution (-theta,0) then to show that -min(ui) be the sufficient…

Q: let z- 57 dy .. dy By chain Ruie

A: The objective is to find the second derivative using chain rule.

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…

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A: Given that f(x,y,z)=xyz-x2z+yz2. We need to find : i)fxz. ii)fzz.

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: Use linearization to approximate In(1.2).

A: we can use the following formula for approximate calculations: f(x)≈L(x)=f(a)+f′(a)(x−a). where the…

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 S,(x) = 2x³ – 3x² + 3x – 4, 0<x < 1, S,(x) = x³ + b,x² + c,x + d,1 sxs 2. Find b,, C1, d, that…

A:

Q: 7) If A = xz³i – 2x²yzj + 2yz*k, find VxA at the point (1,-1,1).

A: Since the student has posted multiple questions and does not mention any specific question, so we…

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: Utu = c²uxx , u(0, t) = 0, u(1, t) = 0, u(x,0) = 0 U¿(x,0) = x² – 2x, 00 t> 0 t > 0 0sx<1.

A: Given P.D.E

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A:

Q: Show that f10 fdx + gdy = S6 10 5a*y²dx + 2yx³dy is independent of path •(11,–7) ,-10) • (11,–7)…

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: Find the clamped cubic spline that interpolates (0,0),(1,1),(2,2) and satisfies the condition: s’(0)…

A: We have to find clamped cubic spline that interpolates (0,0),(1,1),(2,2) and satisfies the…

Q: 5. Show that xZx + yZry = yezy if z= xy + y In xy

A:

Q: Show that there is no Hamiltonian path inCay({(1, 0), (0, 1)}:Z3 ⨁ Z2)from (0, 0) to (2, 0).

A:

Q: round (cov (DFRAME), 2) M N 0 M 2.71 -1.33 0.38 -1.20 0.78 N -1.33 2.89 -1.44 -0.89 0.38 -1.44 5.60…

A: The covariance between two variables say, X and Y is denoted by Cov(X,Y). The covariance between X…

Q: Compute the Wronskian for 2t^2y''+3ty'-y=0

A:

Q: onsider two points (x0, y0) and (x1, y1). Prove that the first order Lan￾grange polynonial is…

A: There are two points (x0 , y0) and (x1 , y1) ,now prove that the linear Lagrange interpolating…

Q: 3,4 show that the integsal (Xy°ty%dx + 3) Independent of the path joining the peints (1,2)and 3,4).…

A: A function F is path independent if it is conservative. And if a function F is conservative then…

Q: s convex.

A:

Q: 5. Define the terms : Skewness and Kurtosis.

A: In statistics there are two types of measures namely measures of central tendency and…

Q: Uyy=4Uxx , U(0,y)=U(5,y)=U(x,0)=0 Uy(x,0)=3sin(2pi x)x)-2sin(5pi x), y>0

A:

Q: 2. Solve the following Cauchy problem: u, + 2ru, - u=a+3ye" with u= 2r - 1 on y=-

A: We have to solve the given Cauchy problem.

Q: > round (cov (DFRAME),2) M N M 2.71 -1.33 0.38 -1.20 0.78 N -1.33 2.89 -1.44 -0.89 0.38 -1.44 5.60…

A: A linear regression equation of Y on X can be expressed as : Y = a+ bX  where a and b are estimated…

Q: Compute the indicated 3 X 3 determi­nant using cofactor expansion along any row or column that seems…

A: Compute the indicated 3 x 3 determinant using cofactor expansion along any row or column that seems…

Q: Q)is a) x^2=y^3 reflexive antisymmetric Transitive  Explain it correctly,solve only when know…

A: We have to find the correct option