1 0> 6(x2+y²)³ across the closed curve C defined by the region in polar coordinate Using Green's Theorem, find the outward flux of F =< - inequalities given by 1

Q: 1. Let k be a nonzero constant. Show that the equation of the tangent plane to the surface xyz = k…

A:

Q: Determine a region of the xy-plane for which the glven differentlal equation would have a unique…

A:

Q: 2-) Let T be the region bounded by the coordinateaxes and the line wwm m www X+y= tin the xy-plane.…

A: Given that  x+y=π. That is the graph is y=π-x. Now the region T is bounded between this line and the…

Q: Let S be the surface of the solid hemispherical region above the plane z = 0 and below the sphere…

A:

Q: QUESTION 1 Let D be the region of the Xy-plane with points on and inside the square with vertices at…

A:

Q: 3. Let f(x, y) be a differentiable function in the variables x and y. Let r and 0 the polar…

A:

Q: 3. Determine the absolute maximum and minimum values of f(x,y) = 2+4x-2x²+4y-y² %3D on the region R…

A: We have to solve given problems:

Q: 9. Find the flux of F =(x, y, z²) across the solid that is enclosed by the hemisphere z=4-x² -y' and…

A: here solid is enclosed by hemisphere z=4-x2-y2   and the plane z=0 and F=x , y , z2

Q: Q. Consider the second order Cauchy- Euler DE x' y" + Bxy' + y = 0,x > 0, where Bis a constant a)…

A:

Q: (a) Evaluate ([ Á.ds where A=(x+y²)î-2xj+2yzk and s is the surface of the plane in the first octant…

A: For the detailed solution of the problem follow the next steps.

Q: [6 marks] Let Tbe the solid region in the first octant bounded by the circular cylinder Sq:z = V4 –…

A: First, let us find the divergence of the given vector field.…

Q: z4 + z? [()] Find and classify the isolated singularities and zeros of f(z) %3D 24-1

A:

Q: solid Q bounded by the surfaces S1:x² + he first octant

A: We have to choose the correct answer from the given option according to the given condition

Q: 4. Compute the area of the surface formed when f(z) = 2+cosh(z) between 0 and 1 is rotated around…

A: 4.0≤x≤1y=2+cosh(x)dydx=sinh(x)A=∫ 2πy dsA=∫012π[2+cosh(x)] 1+sin2h(x) dxA=∫012π[2+cosh(x)] cosh(x)…

Q: 3. Let X1,., Xn be iid Uniform(0, 3) where 3 is an unknown parameter. You can following fact without…

A: given that

Q: Using divergence theorem evaluate || F.n dS, where S 2xyi + yz?j + xzk and S is the surface of the…

A: Divergence theorem:              ∬F·nds =∫∫∫divFdv     where, divF = ∇·F…

Q: 13.6 - Surface lIntegrals 1. Let S be the surface formed by graphing g(x, y) = x + y +1 on the…

A:

Q: Hw.3 3 Find the areas for the following Vegions: Region boundded by y=x y , and Region bounded by…

A: To find the area of the following region :-

Q: 18) (uoe Disk Method) Find the voleime of the senerated by revoluing the region bounded bay the…

A:

Q: 3. (15 pants) Evaluate the line integral Y ds where C is part of the parabola y = x² from (0,0) to…

A:

Q: # 1-2: Let Rbe the region bounded by the curves y=x and y 0, x=3. beobom ai onotl a vd boeo ioinols…

A: We will solve the first part, For this we are going to use double integral to find area bounded by…

Q: z- 2z + 2 or f(z) : z = 2 is a %3D Z-2 simple pole double pole essential singularity removable…

A:

Q: pls explain to me step by step and dont skip any steps. thanks

A: To prove that the system is asymptotically stable under the given conditions.

Q: 1. Let z = f(x, y) be defined by the given equation. Find the total differential of z at any point…

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

Q: 2) The region is defined by y= sin x, y = 0, x= 0, x = T. Rotate the region about the: a) x-axis b)…

A: Since we only answer up to three sub parts. We’ll answer the first three. Please resubmit the…

Q: 2 3 3 Find the area of the surface z = = X2 + y2 3 where 0 < x 1, 0 < y < 1

A:

Q: (a) In electrostatics, the electric field lines can not form any closed loops. However, in the…

A:

Q: 2 : Let S be a closed surface enclosing a volume R. Let F = fVg, where g(x, y, z) is a harmonic…

A:

Q: h(x, y) = Let f(x, y) = 6 - 3y³ - yx² + 2x² + 2y and 2x² + y². a) Find all the local maximum and…

A:

Q: 1. Let f(x, y) be a differentiable function in the variables r and y. Let r and 0 the polar…

A:

Q: Find the absolute minimum of f(x, y) = 3y/ry on the region R= {(a,y)| - 4 <a S-1, -5 <ys-4}. Express…

A: Given:           f(x, y) = 3yxy        on     R=(x, y)| -4≤x≤-1, -5≤y≤-4 To find:           The…

Q: B is counterclockwise boundary of the region that is enclosed by the x-axis, the y = x - 2, and the…

A:

Q: 4. Given an example of a change of coordinates z= r(s,t), y = y(s,t) where every region in the st…

A:

Q: 1. Solid S is bounded by the ff. surfaces. Sketch S and label its boundaries. x = y² + ²-4,…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 3. An R region of the XY plane is shown below: y = -8/a 2y +z = 4 y=-1/2 2y +a= -1 R If A is denoted…

A:

Q: (x², y², z(x² + y²)) around any closed curve on the surface of Show that the circulation of F = the…

A: Circulation of vector field F around a close curve C = ∫CF.ds If parametric equation of curve C…

Q: Pls explain to me step by step and write clearly. Thanks a lot

A: Rewrite the given nonlinear two dimensional system as follows. x’ = x + y–x (x2 + y2 ) and y’ = – x…

Q: 1. The surface integral of a scalar function can be given in a particularly simple form when the…

A:

Q: -1 -x and the curve x = 10 – 2y. 8 4. Compute the area of the region enclosed by the lines y = x and…

A: The solution are next step

Q: Q. Consider the second order Cauchy- Euler DE x*y"+ Bxy' + y = 0,x > 0, where Bis a constant a) Find…

A:

Q: 2) Evaluate the line integral I = F-dř, where F = (xy² + z) î + (x²y + 2) j+ x k, along the…

A:

Q: 1. Solid S is bounded by the ff. surfaces. Sketch S and label its boundaries. x = y + z −4, x=8-5ỷ…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: A surface D is defined parametrically with the equations                             x=4 u2+v2…

A: Let S be a smooth surface defined parametrically by  r(u,v) = &lt;x(u,v),y(u,v),z(u,v)&gt; where u…

Q: EXAMPLE 2 Use Stokes' Theorem to compute the integral SScurl F dS, where F(x, y, z) = zxi + yzj +…

A:

Q: a) Find the global maximum and minimum for the function x – xy +y in the square (both inside and the…

A:

Q: 13) Parametrize the boundary curve of the surface given by r(r, 0) = (r cos 0, r sin 0, (4- r2)) for…

A: The parametric equation of the surface is given as follows: rr, θ=r cos θ, r sin θ, 4-r2, where…

Q: 4. Let S be the boundary of the “orange wedge" given by polar coordinate ranges 0 < p< 1, 0 < ¢ < n…

A:

Q: H-S Integrate the fallswing funCtini aver the given regionr. R: is the triangle cut from the first…

A: Evaluation of the integral

Q: 9. Use the divergence theorem to find F.dS where F = ry'i+x sin zj+z°k and S is the surface of the S…

A: use divergence thm and cylindrical coordinate

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.