Prove or disprove: Vx € Q, Vy e Q, 3z E Q, (x < y) → (x < z< y).

Q: Let X (2,3. 4) and de fined metrie on X as d(x, y) = |-y Find open ball B (2.2) = (0) O (2) 0 2.0…

A:

Q: Show that the function u e(xy) + Vry V(y/x) provides the quation = 0. dy?

A: Again differentiate,

Q: Let f(x,y, z) = xtan (Vyz)- sin(e*) , evaluate zy %3D дудхда

A:

Q: Let f(x, y) = xcosy- y'e*y. fry at (1,0)is equal to: %3D | -2/3 -2 1

A:

Q: Find ôz|ðu and ôzlôv for z=4e* In(y), x=ln(ucos(v)), y=usin(v) at the point (u, v) = (2, 7 | 4).

A:

Q: D Find the Valve of K So that the fallowing Where u= (XxXz) V= (YY) inner praduct in an.

A:

Q: d. .2 The solid bounded by the cylinder x+y = 9 and the planes z = 0 and z = 3- x. %3D

A: The solution of the problem is given in the next steps.

Q: Determine la derivada direccional de f (x, y) = y In z en el punto P (1, 4) en la dirección de v = i…

A: Topic:- calculus

Q: Utt = 8uxx for 0 < x < ™ u(x, 0) = x² u(x, 0) = 1/2cos(8x) Uz(0, t) = u„(T, t) = 0 %3D II

A: The given P.D.E is                            utt=8uxx for…

Q: = a + zy", z - w* + w, y I = uu" + w", y u+ ve fi az Find when u = 1, v 2. w=0 = %3D H.

A:

Q: Evaluate the integral ∫c(2x-y)dx+(x+7y)dy along the path C, defined as y=9-x2 from (0,9) to (3,0)

A: Given ∫c2x-ydx+x+7ydy  where y=9-x2  from 0,9 to 3,0 Parametrize C by xt,yt=t,9-t2 and 0≤t≤3

Q: Hiw Prove that c=z²,'s coutinuous at z=z. O prove that: if Z#Z0 is dis continnity at Z=Zo, where 2o

A: (1) Calculate the RHL and LHL for the function f(z).…

Q: Evaluate | CurlF nds F(x,v,z) = - yzi + xzj – xyk, and S is that part of the cylinder 4= x² + y²…

A: Given function is  Fx,y,z=yzi+xzj-xyk To evaluate ∬SCurlF·nds where S is the part of the cylinder…

Q: u,v) = ve*tv, and z(u,v) = (u+v)cos v?. OG nd and by using multivariable Chain Rule method. du u=1

A: Given: Gx, y, z=e2x+y+3zxu, v=u lnu+vyu, v=veu+vzu, v=u+v cos v2  To Find: To find  ∂G∂uu=1v=0  and…

Q: Let f(x, y) = xcosy-y e*y. fry at (1,0)is equal to: %3D 1

A:

Q: If f(x, y, z) = In(x7 + y +2)+V + y + z), then find fr, fy and fz at (1, 1, 1). %3D

A:

Q: Let w=x² +3y² + 2z² where x=rcos, y=rsin 0,z=5t find dw dw ar' at

A:

Q: c) Let f(r, y) = Vlry| Prove that f(r, y) is not differentiable at point (0, 0).

A: Given a function : f(x,y)=xy We need to show that f(x ,y) is not differentiable at (0 ,0). Let's…

Q: Find the domain. y-Vx Lütfen birini seçin: a. Df = {(x,y): x < 0 ve y < vx} b Df = {(x,y): x < 0 ve…

A:

Q: If y and z are functions of u and v, then the Jacobian of the function transforming (x, Y, z) → (x,…

A:

Q: Wyx %3D If w = e* + x In y + y In x prove that Wgy

A: Consider a multivariable function . Then the derivative of the function with respect to x is the…

Q: Let f(x,y) = xsin(xy), then fx(x,y) = O sin(xy) + x²cos(xy) O x²cos(xy) O sin(xy) + xycos(xy)…

A:

Q: Show that if f(x, y) is homogeneous of degree n, then                                     xfx(x, y)…

A: It is given that fx,y is homogeneous of degree n,

Q: Solve the problem with Neumann boundary conditions, Ut – Uzz = 0, x,t > 0| u(x,0) = f(x) и, (0, t) —…

A: As given by the question There are given that the equation: ut-uxx=0, x, t&gt;tux, 0=fxux0, t=0 And,…

Q: a) Evaluate the line integral S. (2x – y) dx – (x + 3y) dy, where C is a straight line from (1,1) to…

A:

Q: Suppose that u € C² (R²) and u(x, y) = 0 everywhere on the boundary of the square ((x,y): 0≤x≤ R,0 ≤…

A:

Q: Let f(x, y) = xcosy - ye*y. fry at (1,0)is equal to: -1

A: See the attachment

Q: (h) Vx E R, 3y E R, (x + y > 0 or x + y = 0). (i) Vx E R, 3y E R, (x + y > 0 and x + y = 0). (j) (Væ…

A: .

Q: (a) Let f(r, y) = x - 3ry + 18y, where 3r?y- y- 6x = 0. Prove that f(r, y) has extrema at the points…

A: Calculate partial derivative of f(x,y) with respect to x and y ,

Q: Show that the function u = p(xy) + VrY v(y/x) provides the uation x2 = 0. dy?

A: First find the partial derivative of the given function with  respect to x :

Q: Let f(x, y) = xcosy-y e*y. fry at (1,0)is equal to:

A:

Q: Integrate h (x. y) = yi+xj over the indicated path: r(u) = ui+ u²j. ue [0, 1).

A: Given hx,y=yi+xj and ru=ui+u2j, u∈0,1 We have to integrate hx,y=yi+xj along the path ru=ui+u2j…

Q: -H.. OProve that fcz) =z²,s coutinuous at z=z, O prove that: if Z#20 is dis continnity at Z=Zo,…

A:

Q: If X and Y are two independent RVs with f (x) = e*U(x) and f „(y) = e U(y) and Z = (X – Y)U (X – Y),…

A:

Q: . Given: WZ 1 ZY; WX 1 XY; WX = YZ Prove: Wz || XY Y W

A: Since, we have been given that WZ ⊥ ZY , WX ⊥ XY and WX ≅ XYOur Aim is to prove that WZ  ∥ XY

Q: Solve the problem with Neumann oundary conditions, - Uxx = 0, x, t > 0 u(x, 0) = f(x) ux (0, t) = 0…

A:

Q: Solve ut = upx in the interval [0, 5] with u(0, t) = 0, and u(5, t) = 1 for t > 0 and u(x, 0) = 0…

A: Hi! As per norms, we will be answering only the first question. If you need an answer to other then…

Q: Consider p(x, y, z) = 2xyz - x²y³ v(x, y, z) = xy² + y sin(z) F(x, y, z)= F₂(x, y, z)i + F₂(x, y,…

A: Let F→=f1, f2, f3. The gradient of the scalar field: g is defined as: ∇g=∂g∂x i^+∂g∂yj^+∂g∂zk^. The…

Q: dz for z = da z In(zy) + y, y = c os (x² + 1)

A:

Q: f(z) dz where a inside r= z-a

A:

Q: Show that F(x, y, z) = (y² – e* sin z)i + (2xy + z)j + (y – e* cos z)k is conservative and hence…

A:

Q: D.Prove that y y(2)= U12,9)+ jve (2,4) anelyli the loplale's as z, than Guetion u and v Satiglics

A: Consider an analytic function f(z) of the form . Then f(z) will satisfy the Cauchy-Reimann equation…

Q: Qz: IF U=h cx,g )= Lnce+ ě).show that %3D Sy

A:

Q: Let E be the upper half of unit ball E = {x2 + y2 + z2 ≤ 1, z ≥ 0}. Compute ∫∫∫Ez dV.

A:

Q: Evaluate f(x, y, z) ds. Js f(x, y, z) = x2 + y2 + z2 S: x + y = 36, 0 SxS 6, OszS X %3D !3!

A: To evaluate:

Q: Let f(x, y, z) = x arctan z. Then solution.] af Əzəy (2,3,1)= a In 2 where a = [Show

A: Find the value of a

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.