2. S → (T → U) U → -U (V → S) ^ (W → T) .. V → ~W

Q: Find the line of best fit for x: 2 2 68 10 y: 01233 O ŷ= 0.344x+0.125 %3D O ŷ = 1.29x - 3.14 %3D Oŷ…

A: The regression is a linear relationship between one dependent variable and one or more independent…

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 =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: Evaluate: S, Vte-t² dt.

A:

Q: find in Euler's way 2x ! y(0.1) de y(0)=1 , h=0.05 y' = y -- y

A: The general form for Euler's method is given by yn=yn-1+hfxn-1,yn-1.

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

A:

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: cosulen Dhe probubily densty functren OTherwise which randen werclde Xfellews Find pobebility Tht

A:

Q: U = kuzx for 0 0, u(0, t) = u(L, t) = 0, u(x, 0) = x(L – x)

A: Given that, ut=kuxx , 0<x<L, t>0u0, t=uL,t=0ux, 0=xL-x This is  the heat conduction problem…

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: Compute x 2z ds where C is the line segment C from (0,6,–1) to (4,1,5).

A: The given line segment from   to   can be represented parametrically as: , , and , for    Using the…

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: followinp serves Dedermine is he conditionelly , I converye your work ond justify your absdlutely…

A:

Q: Let X and Y be independent and distributed as N(u, 1). Is T = X-Y sufficient?

A: According to factorization theorem, If the likelihood function L(x,θ) can be expressed in the form…

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: Queston #o 4 Show that X, Ixe, where x, and Xe E IR X= (1,1,1, -1) Xz = (4,2,2, -1) %3D

A:

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: 13. - (In t ² )º t dt

A:

Q: 20. Let -(). -- (). (). u = w = If au + yv = w. (x, y E R), then a - y = (A) 2/3 (В) —3/2 (C) 3/2…

A: To find  The value of x-y

Q: Compute ƒxz and ƒzz for ƒ(x, y, z) = xyz - x2 z + yz2.

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

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: Show using MGF technique that if Z, - N(0,1), for i = 1,2,3,4,5 , then U = Ez - x² with 5 degrees of…

A: Using the MGF technique we have to prove that : U = ∑i=15Z2i ~ χ2 with 5 degrees of freedom, If Zi ~…

Q: 2. Integrate: S w5 V7+ w3 dw 3. Find S (6-+ - sV) de

A:

Q: In Exercises 13–16, find and sketch the level curves ƒ(x, y) = c on the same set of coordinate axes…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

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

Q: Compute 1. % 1+ vår + g2 dr, lal 2 1+ " 2. 1+ V2r-

A:

Q: Thene m for Voritly functiom Mean Valne fex) 2. 3X -4 +S the

A:

Q: (x) = 3x +12x+2, %3D ues of a, b and c such that

A:

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

A:

Q: 12. Prove: ΔUΧΖ-Δ AUXZ AYVZ ~ Z.

A: Given: chord UXChord YVand the Center ZTo…

Q: 2 la), Pu (aw by Re currence relation

A: We have to find out P2(x) and P4(x) by recurrence relation. We know that the generating function…

Q: 9. For n = 1,..,n, let X, be independent r.v.'s such that %3D P(X,=1)= p,, P(X,=0)=1- p,- Under what…

A: Hello! As you have posted the different questions, we are answering the first question (9). In case…

Q: 2 dt 22. Evaluate o v9– 2t² 2 dy 3-y³ 24. Evaluate o v8-y'

A: 22)I=∫0129-2t2dtt=32 udt=32 duI=∫29-9u2 32duI=2 ∫11-u2 duI=2 sin-1uI=2 sin-12 t301I=2 sin-1(23)

Q: -64- Eke n Calcul afe th udlue of Z.Z ?

A: according to company rule we answer only first question and rest can be reposted.

Q: 7) [[3embch5y] dvl [jel*5) dy] „In[sec h 5y]

A: Using rule of logarithm &amp; integration formula of sech(x)

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

A:

Q: Show for all x, y in R |x+ys]xl + ]y!

A: consider left hand side  and use the result x=x2 x+y=x+y2=x2+y2+2xy≤x2+y2+2xy≤x+y2=x+y

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: 1 If f(x, y,z)= of then x- y- 3z ду

A: Differentiate wrt y.

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

A:

Q: Verify the chain rule for jacobian, if y2 u = x + , v = * y2 %3D

A:

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}

Q: 2. In AXYZ, PQ || XY . If XZ = 15, YZ = 12, and ZQ = 8, what is ZP? 2.

A: Use concept of similarity. In similar triangle, ratio of corresponding side are equal.