Determine las primeras derivadas parciales de la función en el punto (1,2) (u, v) = z*y - 3yA O(1,2) Of(1,2)

Q: Use Green's Theorem to find f. [(2x – y+ 4) dx + (5y+ 3x – 6) dy] around a triangle in the xy plane…

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Q: exist. :) Compute the linearization of f(x, y) at the point (x, y) = (1,1). %3D

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Q: 3. Compute the scalar line integral 3 y – xz ds where C is the line seg- ment from (0, 1, 1) to…

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Q: What is the normal vector, n for S is a surface of x +y² +z² = 36 in the first octant? %3D

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Q: Exercise (2): Calculate S. xydx + 3y*dy where C is the curve in xy plane, x = y² from (0,0). to…

A: We have to find the line integral

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).

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Q: 1) Evaluate the line integral Fdr where F(x, y, =) = (x+3y, 2y +z, xy) and y: line segment from…

A: Here, F→(x,y,z)=x+3y,2y+z,xy and γ: line segment from (2,1,3) to (3,3,5) We need to evaluate ∫γF→dr→

Q: Bounded by the planes z= x, y =x, x+y=2 and z= 0

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Q: Glven: XY and ZW Intersect at polnt A. Which conJecture Is always true about the glven statement?

A: as given that XY ↔ and ZW↔ intersect at point A. so, here we understand few terms which is given in…

Q: A rectangular plate is bounded by the lines x = 0, y = 0, x = determine the potential distribution…

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Q: Evaluate ze*²+y²+z? dV, where E is the portion of the ball centered at the origin of radius 5, x2 +…

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Q: What is the value of F.ds, where F = 4xz,- y° i, + yz, ? Here, s is the surface bounded by x = 0, x…

A: Here function is given find f.ds as below

Q: Aşağıdaki alıştırmalarda, f., fy ve fiyi bulun. 23. f(x, y, z) = 1 + xy² – 2z2 25. f(x, y, z) = x -…

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Q: Evaluate the line integral / x°z ds, where C is the line segment from (0, 2,4) to

A: Line integral: - The function to be integrated is determined along a curve in the coordinate system…

Q: : Cven aYv.メニリ34,5,then OFind the P.f. of x (fw): O Evaluste (e) the and 2 non Centeral moment of X.…

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Q: find laplace of f(x,y,z)=2x3y2z2

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Q: İki noktalı Gauss kareleme yöntemini kullanarak S dx integraline 1+16x4 yaklaşık değer bulunuz. 2…

A: we have given by integral ∫-12128x21+16x4dx we have to solve the integral by using two-point…

Q: ofind the Veelles Such that of A ond R

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Q: please explain this solution (orthogonal projection onto W) 1 1 1 1 1 1 1 0 0 1

A: Given: To explain the given solution as follows,

Q: Calculate moment generating function of J = Y + Y2 + Y3 to determine distribution of J and its %3D…

A: Given that Y1, Y2, and Y3 are independent geometric random variables with parameter p.

Q: f(r, y, z) = byz In(4ry) %3D fz = fy = た=

A: Given:

Q: t in 30 minute please duopoly with homogeneous goods. There ar

A: When there are only two firms in the industry, it is in their advantage to collude and set the price…

Q: Integrate Xy ed २ over the triangular region with vertices: (0,0), ), (0,8) (0,16)

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Q: How would I solve ∭xzdV, where E is bounded by the planes z = 0, z=y, and the cylinder x2 + y2 = 1…

A: Solution is given below:

Q: Let S be the surface parametrized by R (u, v) =< u, uv, uv

A: It is given that, the parametrized surface is R(u,v)=u, uv, uv2, 0≤u≤2, 0≤v≤3.  We have to calculate…

Q: Calculate fc((3x + 5y) i + (3x + 4y) j) - dr where C is the circular path with center (a, b) and…

A: According to the greens theorem:

Q: Compute (ax + by² + cz) dS over the sphere x +y +z² = 1.

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Q: 2. Integrate f(x, y) = sin /x2 + y² А. over the closed unit disk.

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Q: 10. Para resolver la siguiente ecuación diferencial: y" + 2y' + y = 0 con y(0) = 1; y'(0) = 1 Se ha…

A: The solution of differential equation is given by using Laplace transform and partial fraction…

Q: Verify Divergence Theorem for by co-ordinate planes and the plane 2 x + y + 2 z = 6. F = (x+ y³) i –…

A: Given that F=(x+y2)i-2xj+2yzk The divergence theorem is, ∭FdV=∭∇Fdxdydz On surface S1, y+2z=6,…

Q: Find the orthogonal trojectories of y(sx +c) = 1.

A: Given query is to find the orthogonal trajectories to y (3x+c) = 1.

Q: Determine the type of points on the x(u, v) = (u, v, u²) surface. Differential geometry

A: Given point is Xu,v=u,v,u2.  This point is of the form Xu,v=fu,v,gu Let Xu,v=xi+yj+zk. Then,  x=u…

Q: How would I solve ∭xzdV, where E is bounded by the planes z = 0, z=y, and the cylinder x2 + y2 = 1…

A: The given equation of the cylinder us x2+y2=1 in the half space y≥0. Calculate the value of ∫∫∫xzdV,…

Q: Find the linearization of f (x, y, z) = xy / z centered at (2, 1, 2). Use itto estimate f(2.05, 0.9,…

A: Our Aim is to find the linearization of f(x,y,z) =xyz centred at (2,1,2).and then using that value…

Q: curve in the xy-plane is denned by the vector valued functic dy in terms of t? dx? where x(t) = 2…

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Q: Integrate f(x,y,z) = x-3y + z over the line segment joining the points (0,0,0) and (2,2,2). %3D

A: Here, we need to integrate f(x, y, z)=x-3y2+z over the line segment joining the points (0, 0, 0) to…

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) Find Ow/ôu and ôw/ôv for w= xy+ yz+ xz, x=u+v, y =u –v, z = uv at the point (u, v)= (1/2,1). 3…

A: If w=f(x,y,z) and x=g(u,v) ; y=h(u,v) and z=t(u,v) then, ∂w∂u =∂w∂x.∂x∂u+∂w∂y.∂y∂u+∂w∂z∂z∂u  and…

Q: 8. Evaluate the double integral // ydrdy where T is the triangle with vertices (0,-1), (0,5), (4,…

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Q: Evaluate the line integral §. xy²dx + 2x²y dy over triangular path with vertices (0,0), (2,2) and…

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Q: Evaluate the triple integral ryz dV, where T is the solid “tetrahedron" with vertices (0,0,0), (0,…

A: Identify the limits of integration from the region. The base of the tetrahedron is in the xy-plane.…

Q: Find div (e" grad u x 7) u=x-y ex at (2,1,0) where and =(x²+1)i + sec¯¹(x² −y)j + 3y²zk

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

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Q: Evaluate the line integral ∫Cx^3z ds, where C is the line segment from (0,3,8) to (8,4,6).

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Q: flz) = Im z is continuous %3D

A: The objective is to check f(z) =Im Z is continuous Or not.

Q: 2. Compute the line integral of E from B(0,0,0) to A(2,1,3) if E = -4xyax - (4y + 2x2)a, + 8zaz. Use…

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Q: 10. Find the work done by the force F=vx +2y y - 7 for a particle that moves between points (-1,0,1)…

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Q: Stress quadric surface of Cauchy g1ven by 6,2 18pr ulge O

A: No, the given is not the stress quadric surface of Cauchy.

Q: Use Green's Theorem to Calculate the Line Integral ſy²dx + x²dy, where c is the triangle o vertices…

A: Given that, the line integral is ∫y2dx+x2dy and the vertices of the triangle is 0,0,4,0 and 4,4. By…