Let f be q functiom that admits contırous second partial denvatives Df (X.Y)=(4x²- 2q²x+ 2q°y ,4y³ + 2q°x=2q²y) 3

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

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Q: If u=f(x2+2yz,y2+2zx).Prove that

A: Given: u=fx2+2yz, y2+2zx Let u=fv, w where v=x2+2yz and w= y2+2zx. Now prove…

Q: If f(z) = 10 V 824 - 2° + 5, find ƒ '(x). %3D O f (z) = 5 (8z“ – 2z° +5) *| O f (z) = 5 (32z° –…

A: The given function is fx=108x4-2x6+5. Differentiate the function with respect to x by the power rule…

Q: Show that |qbu)|&x + 7元? the closed on interval [-元,T」 fo1 -π2 2くだ gluen that glven gux) for

A: Given g (x) = x +x² To find the maximum value of g(x). We can differentiate the function and equate…

Q: and the parmial 58. Find the value of ax/az at the point (1.-1.-3) if the equation +y Inx + 4 = 0…

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

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Q: ) Find the fomily of the equ ation of all lines in 3-space perpen diuler to 2x -y +2u u Given line

A: Family of lines contains parameters.

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: Compute the partial derivatives. f(x, у, 2) %3D 8x4 y7 + z6 af 3 32x 17 +-6 af – 56x ду _6 48x4 y'…

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Q: 93.> (@) Find the complute aud singulak integeal 9 the partial alifferential equation + 3p 2 2 3 px

A: Solution a: Given PDE is z=px+qy+3p2q3 Since give PDE is of the type z=px+qy+f(p,q) which is the…

Q: Find the meteix A of the Lineak teansfoRmati on foom IRto IR . 2. given by x2

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

A: Rrrrrrrl

Q: Verify f U= n1 V = 234 43 snyz %3D +23- 422-24-42- dependend %3D fundlarelly are

A: We know the identity: x3+y3+z3-3xyz=(x+y+z)(x2+y2+z2-xy-yz-zx) --(1) We are…

Q: Compute the partial derivatives. z = In(8x2 + 5y²) * - In(16x + 5y²) az əz ду

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Q: 3) Use Green's Theorem to evaluate o-ydx+xydy where C is the line segment from (-2,0) to (2,0) then…

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Q: Use Theorem 2.4.1 to prove that f(x,y) = 1 - x^2 - y^2 defined in R^2 is concave.

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

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Q: Let UsX +Sinx Deter of X 0n [0,)where ļ Find . derivalire fa 2x+1 x²+7 te tn 6x+

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Q: Find the aven bounded by y=x and y =x+2

A: First draw the graph of the function and find the intersection point of the graph:

Q: Find the rank of A= = xS+ x + invertible. [exham S] O A MOITERUD 225 10-4 and explain why it indic 4…

A: NOTE: Refresh your page if you can't see any equations. .

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: Let X,X2, ,X, be a ranc *(X), = 0*(1– 0)1-x; %3D

A: from above distribution is binomial  f(x)θ=θx(1-θ)1-x  ;0<x<1 E(x)= nθvar(x)=nθ(1-θ)…

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

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Q: If y = xsinx then prove that y''+y=2cosx

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Q: どタ -e -at u Ct) = (a +jwjñ+!

A: To prove that tne-atut↔n!a+jwn+1 It is known that  ut=1 , t>0=0, t<0 Therefore,…

Q: (ii) Verify Cauchy-Goursat theorem for f(z) = 5 sin 2z if C is the square with vertices at 1土も-1土。

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Q: Find the orthogonal trajection of the family of y=ax

A: In mathematics an orthogonal trajectory is a curve, which intersects any curve of a given pencil of…

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: 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: 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

Q: The partial differential equalion formed to om the (x -af + ÿ +(2-65 = 16 is nelation 9. %3D = 16

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Q: Find the first partial deravatives of the function

A: Since, only question no. 21 is clearly visible in the image you have provided, that’s why we are…

Q: Find the Linearizat ion of Non lineah Relations hip Y= (ax+

A: This is the problem of linearization, application of differential calculus.

Q: /show that fo-1x is-Contindals everywhere.

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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: Suppose that U(x; y) = xe' + ysin z, and that x, y and z can be measured with maximuma possible…

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Q: Let D, be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

A: Dx(f)=8x+5 Apply integration both side  ∫Dx(f)dX=∫(8x+5)dx   f(x)=(8x2)/2 + 5x +c (here c is the…

Q: LetX1,X2,...beindependentrandomvariablessuchthat

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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: 1. Use the definition of partial derivative as the limit of a difference quo- tient in order to…

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Q: Compute the value of f.dr If F= -yi+xj and c is a from (-1,1Y to CI,1) %3D SemICirele

A: Proceed as shown below

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

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Q: 1 If f(x, y,z)= of then x- y- 3z ду

A: Differentiate wrt y.

Q: 3)suppose fle) isadifferentialle fmehon on the intervall E-7,J Such that Hl-7) =4 and fl)=1.…

A: Intermediate value theorem

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

Q: Compute the convolution y(n) = x(n) * h(n) , Where x(n) = {1,1,0,1,1} and h(n) = {1,-2,-3,4} , Using…

A: Given: Given convolution expression is Y(n)=x(n)*h(n) x(n)={1,1,0,1,1} h(n)={1,-2,-3,4}