f (u, v) = (u? + v?) is not homogeneous O homogeneous 3rd degree O homogeneous 2nd degree O homogencous 3/2 degree

Q: Continuity for Three VariablesAt what points (x, y, z) in space are the functions in Exercises 35–40…

A:

Q: Integrate f (x,y,₁/2) = 2² +12y +7 over the cuna 7 (t) = (²1 +31²) + (1², 1st sz - 6+² try to sketch…

A:

Q: 24(z + i) (z - 4)5 (22 + 4)(z – 5) f(2), -dz integral value calculate. Y. F(2) c : |2| = 3 ve f(2) =…

A:

Q: Find the area of R = {(x,y) = R² : x € [−1, 2], y € [x²,x+2]} integrating first along horizontal…

A:

Q: Find the potential u(x, y) for u +u =0 in the rectangle 0<x< 2 and 0 < y s 2, if the upper side is…

A: The given problem is to solve the potential u(x,y) Laplace partial differential equation, we have to…

Q: If F= represents the flow of a liquid through a parabolic cylinder S: y=x, 0sxs2, 0szsl. That is…

A: If F→=y2,-x2,z2 represents the flow of a liquid through a parabolic cylinder S:y=x2,0≤x≤2,0≤z≤1.…

Q: Find the total differential of W = x^4 y^3 z^2 + x^3 Y^2 + x^2 z +y + 3 at (2,1,1)

A:

Q: The solid bounded by x = y? – 1, z = 1 – y², z = 4 – x, and z = 0.

A: Given that,

Q: (A) Find div (e grad u xf) at (2,1,0) where x-y and =(x²+1)i+sec¯¹(x² −y)j + 3y²z. k YZ 11=

A: What is grad, div and curl: Gradient, divergence and curl are important in vector calculus. Gradient…

Q: In Exercises 11-16, use the Chain Rule to evaluate the partial derivativeat the point specified.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Integrate F(x, y, z) = z - x, over the cone z = sqrt(x2 + y2), 0&lt;= z &lt;=1

A:

Q: Find the area of R = {(x,y) € R2 : x E [-1, 2], y e [x², x+ 2]} integrating first along horizontal…

A:

Q: f(x, y, z, w) = (1+x+ sin(z − 2y), ez-w, 2z+tan(w+x²)).

A: we have to find the approximation of ƒ at the point P = (0, 0, 0, 0).  For this we use the proper…

Q: se-x 0 <x < 00 Q4/ Let X,,X2 and X, be iid with common pdf f(x) = { е. w and let Y, X1 Y, X2 , Y, =…

A: The answer is given using the concept of pdf.

Q: f(z) = Cosz %3D ,0< Izl f(2) = sinz 3D 0< zl %3D f(z) = e-V, 0< Izl %3D

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: rsin z O Find V2 +t+t2) dt.

A:

Q: Integrate G(x, y, z) = z2, over the hemisphere x2 + y2 + z2 = a2, z&gt;=0.

A:

Q: If f(x, y)is integrable function on the rectangle R = [a, b] x [c, d] where [a, b] on the x- axis…

A: In the question it is asked to show how the two double integrals are equal to each other.

Q: 3. The solid bounded by z = 0, z = 1 – x², z = y and 2y + z = 12.

A: Given that  Region z=0,z=1-x^2 and 2y+z=12  To form a triple integral

Q: 2. Evaluate the triple integral where E is the solid bounded by y = 2x² + 2z² and the plane y = 8.

A: A detailed solution is given below.

Q: f (x, y) = xlx - alny is %3D O homogeneous 0 degree O not homogeneous O homogeneous 2nd degree O…

A:

Q: Suppose F = ∇ * A, where A = (y + sqrt(z))i + e^(xyz) j + cos(xz) k. Determine the flux of F outward…

A:

Q: Integrate counterclockwise z + 6 dz, C: |z – 1|= 4 Z – 2 z + 6 dz 2 ||

A:

Q: Among all rectangular regions 0&lt;=x &lt;=a, 0&lt;=y&lt;=b, find the one for which the total…

A:

Q: Find fz and fy- f(x, y) = Te“ dt f„(x, y) %3D S,(x, y) =| %3D

A:

Q: (1) Evaluate the triple integral I zyz dV, R where R = {(z, y, z)| 0 < z < 3, -2 <y< 1, 1< z < 3}.

A: We will use simple Integration rules to solve this triple integral.

Q: The integral JJI eV 4x2 + 4y² + 4z² dV = mt, where R is the solid hemisphere with x2 + y? + z² < 11…

A:

Q: 2) Find the outward flux of F across the region D where F(x, y, z) = (In(x² + y²), –tan'(), zVx² +…

A:

Q: Find the area of R = {(x,y) = R² : x € [-1,2], y € [x²,x + 2]} integrating first along horizontal…

A: The double integration in the horizontal direction is ∫ab∫g(y)h(y)f(x,y)dxdy The double integration…

Q: Evaluate fz² In z dz using integration by parts O² Inz-+c Onz-+c Onz-+c 2²lnz - 2 + c 12 21

A: Solution:  step-1: Evaluate ∫z2*lnz dz using integration by parts                Formula for…

Q: ây _ở: x>0, t> 0 where y (0, t) = 1, y (x, 0) = 0. Find the bounded solution of

A:

Q: ds k(4nr). dt --Select-- %3D volume dV k dt surface are ds - ). dt dV dt dV = k(4tr²). dt

A: Given evaporation rate proportional to surface area Use formula of volume and surface area to find

Q: Use Chain Rule to find ds given w = Vr² – 2y + z² and r = cos (st), y = -2s Int and z = s –

A:

Q: Find the generated volume f(x)=sin(x) and the lines x=0 and x=π and rotate about the x-axis V=π^2…

A:

Q: The solid bounded by z = x, z = 2 – x², z + y = 3, and y = 0

A: Volume of a solid is obtained using triple integration by the formulae =∫∫∫dx dy dz The solid is…

Q: 2. Let z = g(x, y) = e" cos y + y In(x – 1). %D Use local linear approximation to estimate g(1.99,…

A:

Q: 9. The solid bounded by x = 1 – y?, z = y², x = 5, and z = 9.

A:

Q: Q2 Evaluate the line integral | F•ds where F = 2xyi +(x- y²)j and C is (a) y = x from (0,0) to %3D…

A:

Q: y = x, %3D x = y?, 0<x < 1, 0.8 0.6 y 0.4 0.2 0.2 0.4 0.6 0.8 Figura 11.13. Ejercicio 11.17 como una…

A:

Q: | Fug kuote the triple integral SSS 3ydv, where =L(ay.) | os xE2, 0sys lu-x?, 0s2sx.

A:

Q: 3- Verify the properties (HINT Use integration by parts) F[ux] = iF[u] F[uxx] = -²F[u]

A:

Q: 5. If F = (x,2y,3z), the outward flux of F across the boundary of a unit cube (volume equal to 1) is…

A:

Q: 17. Suppose F = V × A, where A = (y + Vz)i + e»²j + cos(xz)k. Determine the flux of F outward…

A:

Q: Find the area of R = {(x,y) € R² : x E[-1, 2], y e [x²,x + 2]} integrating first along horizontal…

A: Given region is   where curves are y=x2 and y=x+2

Q: F(x, y, z) = xyzi+ (2ry+2) j+y°z°k conservative?

A:

Q: Use Stokes's Theorem to evaluate F dr, where F(x, y, z) = x²i+z²j-xyzk and S is z = /169-x² -y² .…

A: As per our guideline we can't use any computer algebra. I calculate both line integral and surface…

Q: h(r, y) = h(0,0) = 0 3x2 + y2 (i) Prove that |h(r, y)| <ly

A:

Q: Prove that (x,y,z)=(2.25,-1.35,0.169) minimizes 1.5 the integral , [w3 – (xt² + yt – z)]² dw

A: We will use basic knowledge of multivariate calculus to solve this question. Note that we are…

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

Q: = In(x) – In(y) + *-y dr r+v Homogeneous O Not homogeneous

A: A differential equation is homogenous if ftx,ty=fx,y.