Let x = s e and y =t es. Compute the Jacobian

Q: Find x, y e lº such that || x || ∞ = 1 = || y || = || x+y 2 || x #y.

A: As per the question we have to find two sequences x, y from the norm-space l∞ such that : ||x||∞ = 1…

Q: Use an appropriate form of the chain rule to find dz dz and du dv 1 z = e"u; x = Vuv, Enter your…

A: Here z is function of x,y and x,y are themselves functions of u,v .so z is composite function of…

Q: Let fxy (x, y) = 6 (x – y) , 0 < y < x < 1. If E (X) = , E (Y) = Cov (X, Y) = then %3D

A: Given,fXY(x,y)=6(x-y) ; 0&lt;y&lt;x&lt;1E(X)=34E(Y)=14

Q: Use appropriate forms of the chain rule to find ðz/ðu and əz/əv. z = e*"; x = /uv, y = 1/v

A: In the question it is asked to solve differential equation using chain rule.

Q: Find the Jacobian (x, y) / d(u, v) for the indicated change of variables. x=u-v², y = u + v a(x, y)…

A: Follow the procedure given below.

Q: こ= (t)} () て= () %3D - (^),J %3D てんn ZトXC

A: →∫eax+bdx = eax+ba + C, where 'C' is the constant of integration.→∫xndx = xn+1n+1 + C

Q: Define: T:P, → R by T(P) = [ p(x)dx. What is the kernel of T ?

A: Given that: T:P2→RTp=∫01px dx

Q: If z = In(x² – 2y), and x=u+v, y= e" , find and du If w=2xy'z', and y =x² +1, z= Vx, find dx

A:

Q: Integrate ƒ(x, y, z) = (x + y + z)/ (x2 + y2 + z2 ) over the path r(t) = t i + t j + t k, 0 &lt;…

A: The equation of the parametric curve (path) is:   Path r(t) = x(t) i + y(t) j + z(t) k   And the…

Q: Let h(y,z)=y(e)^−z. Calculate ∂h/∂y and ∂h/∂z.

A: Given : hy,z = ye-z

Q: Find the Jacobian a(x, y) / a(u, v) for the indicated change of variables. 8u, y = uv x = UV a(x, y)…

A: Given,            x=uv-8u , y=uvTo find : Find the Jacobian ∂x,y∂u,v for the indicated change of…

Q: for for w= rs ,Y=uV S=uーv, find and Jw

A: Given w=rsr2+s2, r=uv, s=u-2v To find  ∂w∂u and ∂w∂v By chain rule,…

Q: for transformation x=au + bv, y=bv+cw, z=cw jacobian value J(u, v, w) = ...

A:

Q: Solve the following relations for x and y, and compute the Jacobian J(u,v). u= 2x + 2y, v = 3x -y…

A:

Q: Evaluate O xy dx + x°dy, where C is the rectangle with vertices (0,0), (6,0), (6,3), and (0,3)

A:

Q: Let z= I= 2e", and y = 3 ln v. Find in terms of u and v.

A:

Q: Use the Chain Rule to find ôz/ðs and ôz/ôt. z = tan(u/v), u = 9s + 8t, v = 8s – 9t as az at

A:

Q: Find the Jacobian w/ respect to UVW X=U(3-v), Y= uv(3-w), Z=Uw

A: Our aim is to find the jacobian of x=u(3-v), y=uv(3-w) and z=uvw⇒x=3u-uv ,   y=3uv-uvw and…

Q: Given u(x, t) = t°e¯ï, compute:

A:

Q: Let u = cos(r + y), x = 2st +t and y = t – 2s. Use the chain rule theorem to compute du for du and…

A:

Q: A function e : X → Y is an embedding if one ond for V

A:

Q: (i) Find the conditional pdf's fyx y and fyly y

A:

Q: , find the Jacobian ?(x, y)?(u, v) for the indicated change of variables x = uv − 2u, y = uv

A:

Q: If z = xe, æe then dz = (e )dx + (ryev" )dy. Select one: OTrue OFalse

A:

Q: If u = 2x - 3y, v = -x + y. Then the Jacobian J(u,

A:

Q: . If x, y E R with x < y, prove that x < tx + (1 – t)y < y for all t e (0,1).

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Use the chain rule to find az az and as at z = (x - y)", x = s?t, y = st? az as az at

A:

Q: Let v f(x,y) and w f(x, y). Choose a correct formula %3! to determine where J is a Jacobian. dv aw…

A:

Q: Consider, 21u = 2x – 3y and 21v = -–x+y Find the value of the Jacobian a (x, y) a (u, v)

A: 21 u = 2x - 3y, 21 v = -x + y

Q: Evaluate O xy dx + x°dy, where C is the rectangle with vertices (0,0), (6,0), (6,3), and (0,3).

A: The solution is given by using greens theorem as follows

Q: Find the Jacobian a(x, y) / a(u, v) for the indicated change of variables. x = e U sin v, y = e-U…

A: Given: The change of variables formula x=e-usinv and y=e-ucosv, To find: Jacobian ∂x,y∂u,v.

Q: d) If U = X + Y and V = Y – X, find i) The Jacobian value of U and V J(U,V)

A: Solution

Q: If u = lx +my andv=mx -ly, show that +m? du), +m²

A: given  u=lx+my   ...iv=mx-ly   ...ii to show that  ∂u∂xy∂x∂uv=l2l2+m2 ; ∂y∂vx∂v∂yu=l2+m2l2

Q: Find the Jacobian a(x, y) / a(u, v) for the indicated ch x = e-u sin v, y = e-U cos v a(x, y). a(u,…

A:

Q: Find the Jacobian a(x, y) / a(u, v) for the indicated change of variables. v), y = (u + v) X = -

A: The formula for the Jacobian is: ∂(x,y)∂(u,v)=∂x∂u∂x∂v∂y∂u∂y∂v

Q: Show that if X and Y are independent rv's, then E(XY) = E(X) · E(Y)

A: we have given that, x and y are independent random variables, then, we will prove, E(XY)= E(X).E(Y),

Q: Let T(r,s,t) = (r cos(s) sin(t), r sin(s) sin(t), r cos(t)) Find the Jacobian of T at (3, π/4, π/3)

A:

Q: Find the Jacobian d(x, y) / d(u, v) for the indicated change of variables. u- v), y =u + v) X = -

A:

Q: If A = 3.4xyâ + (1.7x² – 6.8y)âŷ, the circulation of A around the closed path shown below is

A: In this question, we have to find the circulation of vector A along the given closed field in fig.…

Q: Show thet tegular a S(G) = A(G). G

A: Let us assume that graph G is regular. Now,  δ(G)= degree of the vertex with minimum degree…

Q: Consider ф: C" — C defined by ф(x) %3D х*. a) Kerф %3D (1,-1} b) Kerø = {i,-i} %3D с) Kerф %3D (1,1}…

A:

Q: Let z = f(x, y) where g = e° cos t and y = e sin t. Use the Chain Rule to show: az, a z = e

A:

Q: a) V = R", (x, y) = (Ax) · (Ay) where A e Mn,n is invertible.

A: Given that, V∈Rn,  A∈Mn,n is invertible matrix, i.e  A≠0 we have to show that x,y=Ax.Ay is inner…

Q: In general, E(XY) + E(X) × E(Y), but if X and Y are E(XY) = E(X) × E(Y). independent RVs,

A:

Q: Consider the ARMA(3,1) model represented by y, – 0.8y,1-0.25y,-2 +0.2y,-3 = e, -1.2e,1. (a) Is it…

A: Given the ARMA(3,1) model as yt-0.8yt-1-0.25yt-2+0.2yt-3=et-1.2et-1

Q: Find zx- Zy, given z = x+y

A: Given :            Z = xyx + y   To find :            Zx - Zy   Formula : Quotient rule of…

Q: Find the Jacobian a(x, y) / a(u, v) for the indicated change of variables. x = eu sin v, y = eu cos…

A: To find the jacobian.

Q: dv E={my,)|→<y<4Y<そく4, Osns? そ

A: Given that  Triple integral of z/(x^2+z^2) To evaluate the integral

Q: . If z = f (x, y), where x = e" - e and y = e - e", show that TM UT az x: az az az dy ax UTM UTM UTM…

A:

Q: f(z, y) – zsiny +e, then Vf(r, y) (0, e").

A: