3) Let F = (y+ev=,8x+ cos(y*)) Use a theorem to compute ſ F •dT where c is the boundary of the planar region enclosed by the parabola y = x² and the line x = y, counterclockwise.

Q: Let x and y be differentiable functions of t, and lets = √(x2 + y2) be the distance between the…

A:

Q: Let f(x, y,z) = x² sin y +y e, where x t +3,y = net-1 and z = In 2t. %3D at t = 1 is: dt O -12n O…

A:

Q: Evaluate the triple integral |// xy dV where E is the solid tetrahedon with vertices (0,0,0), (7, 0,…

A: Consider the following: Equation of plane passing through 7,0,0,0,5,0,0,0,10x7+y5+z10=1x ​ranges…

Q: 1. Under the paraboloid = 3z2 + y? and above the region bounded by y = x and r= y² – y

A: Find point of intersection of:  y=xx=y2-y y=y2-yy2-2y=0y=0,2

Q: (1.-13) Show that the line integral (2xy+3)dx +(x² - 4z) dy-4 ydz is independent of path and (0.0,0)…

A:

Q: Evaluate the line integral (x+2y)dx + dy, where C consists of the path C from (0,0) to (3,0), the…

A:

Q: 6. Evaluate the line integral g. x²y² dx + xy dy where C consists of the arc of the parabola y = x²…

A: (a) Direct method The given line integral is ∮C x2 y2 dx + xy dy. The curve C consists of    C1 :…

Q: Use Green's Theorem to evaluate the line integral |(y - x)dx + (2x – y)dy for the given path. C: x =…

A: Let's find.

Q: 1. Show that the problem may be formulated in terms of the velocity potential o(r, 0) satisfying 6,…

A:

Q: Given etye -Z+ xy - e-0, use e =0, use impicit partial denvatve to finid 2ž at the Point (1 2t

A: Explanation of the solution is given below....

Q: Evaluate the line integral f. (2x – 4xy)dx + 3xy – 2x³y)dy over the straight path L joining point…

A:

Q: Consider the finction f(x, y) = 6y² + 4x² – 12xy- 4y. Then: (1,1) is a critical point and f has a…

A: The given function is f(x,y)=6y2+4x2-12xy-4y

Q: 9. Use Green's Theorem to evaluate (e* +y²) dx +(e" +x²) dy where C is the boundary of the region…

A:

Q: Since f(x, y) = 1 + y² and ðf/ðy = 2y are continuous everywhere, the region R in Theorem 1.2.1 can…

A: Given data: We are given that y=tan(x+c) is the family of the solution using initial value y(0)=0

Q: If x, y, and z are lengths of the edges of a rectangularbox, then the common length of the box’s…

A:

Q: 2 Find.all.se.cond.partial.devevatives:. f(x,y)In(3xi+5.y..b.ue sint C.Z-ytan x a..

A:

Q: Evaluate the triple integral xy dV where E is the solid tetrahedon with vertices (0, 0,0), (6, 0,…

A:

Q: Use Green's Theorem to evaluate the line integral (y - x)dx + (2x – y)dy for the given path. C: x =…

A:

Q: Evaluate the line integral f (-y sin(xy)i – x sin(xy)j) dr using the potential function f(x, y) =…

A:

Q: Use Green's Theorem to evaluate the line integral √(x - (y - x)dx + (2x - y)dy for the given path.…

A: Let's find.

Q: 1.13 Evaluate the line integral $ x*dx + xydx where C is the triangle with vertices at (0, 0), (0,…

A: The given function is x4dx+xydy By green's theorem, the integral becomes, ∫06∫06∂M∂y-∂N∂xdxdy where…

Q: 1. Evaluate fL, 2 dv where E lies below the plane z = 2+ 3x + 4y and above the region in the…

A:

Q: 3. Evaluate the line integral y² dx + x²y dy where C' is the rectangle with vertices (0,0), (5,0),…

A: Solution is below

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

A:

Q: Use Green's Theorem to evaluate the line integral (y – x)dx + (2x – y)dy for the given path. C: x =…

A: Given integral is ∫Cy−xdx+2x−ydy where C:x=2cosθ,y=sinθ,0≤θ≤2π. Green theorem is given by…

Q: 8. Evaluate the line integral x dx + xedy where C is the closed path along the triangle in the…

A:

Q: Let w = x°e4y cos(9z). Find the value of dwldt at the point (3, ln 5, 0) on the curve x = 3 cos(t),…

A: Given: w=x6e4ycos(9z)x=3 cos(t)y=ln(t+5)z=6tDifferentiating we…

Q: 1. Show that the problem may be formulated in terms of the velocity potential (r, 0) satisfying r dr…

A:

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

A:

Q: A necessary condition for the functional defined by X2 = dx f(x, Y(x),Y'(x)) to have a local minimum…

A:

Q: Let f(x, y,z) = x² sin y + y e², where x = t + 3,y = net-1 and z = ln 2t. %3D df at t = 1 is: dt…

A:

Q: Assume x and y are functions of t. Evaluate dy for 4xy - 7x+4y3 = - 48, with the conditions dt dx =…

A: Explained below

Q: 5) Find the region in the xy-plane for which (sin x – y)y' = vx- y satisfies the nonlinear existence…

A: A differential equation  y' =f(x,y) will have at least one solution in the region where f(x,y) is…

Q: Evaluate the triple integral III xy dV where E is the solid tetrahedon with vertices (0, 0, 0),…

A: The given integral is, ∫∫∫E xydV Here E is the solid tetrahedron with vertices O0,0,0, A10,0,0,…

Q: (z - 1)dt + (1 – t)dz %3D

A: (4) Given differential equation is z−1dt+1−tdz=0......1. We have to determine the whether the…

Q: 2. Let z = sin(xy) + x siny,x=u² + w² and y = uw. 2a. Compute Vz= when u = 0 and w = 1.

A:

Q: Verify Green's Theorem by evaluating both integrals ам √₁ y ² dx + x² dy = √₂√ √ (³x - dA ax ду for…

A:

Q: Assume x and y are functions of t. Evaluate dy / dt for 4xey = 8 - ln 64 + 6ln x, with the…

A:

Q: 3. Show that the line integral | (r + y)dx + xdy is independent of path and evaluate this integral…

A:

Q: Use the fundamental theorem of calculus for path integrals to evaluate f.(yz2, xz2, 2.xyz). dr where…

A:

Q: The line integral (x+/y) ds , where C is the line segment joining the points (0, 0) and (1, 1) , can…

A:

Q: Consider a potential problem in the half-space defined by z 0, with Dirichlet boundary conditions on…

A: The green function solution to the potential problem with this boundary for Dirichlet boundary…

Q: Let f(x, y,z) = x? sin y+y e, where x = t+3,y = net-1 and z = In 2t. %3D at t = 1 is: df dt О 12п O…

A:

Q: 8. Evaluate the line integral fx'dx + xe 'dy where C is the closed path along the triangle in the…

A:

Q: 17. 6xy dV, where E lies under the plane z = 1 + x + y and above the region in the xy-plane bounded…

A:

Q: 3. Evaluate the line integral / (x+ 2y)dx + x²dy, where C consists of the path C1 from (0,0) to (3,…

A:

Q: 3.4.6 Evaluate the line integral [sin y dx + (x- cos y) dy] taken in the anticlockwise sense, where…

A: Green's Theorem States that  Let C be the positively oriented, smooth, and simple closed curve in a…

Q: 8. Evaluate the line integral (x'dx+ xe"dy where C is the closed path along the triangle in the…

A: Here we have to evaluate the integral ∫cx2dx+xe-ydy where C is the closed path along the triangle in…

Q: 1 Find skewness and kurtosis for the RV X with PDF f(x) = 2T -∞ < x < x.

A: PDF of X,  fX(x) = 12πe-x22, -∞&lt;x&lt;∞ So, μ = E(X) = ∫-∞∞x f(x) dx=∫-∞∞x 12πe-x22 dx=0 [as…

Q: 12. Find the outward flux of F = x*yi-cyj+zk across the boundary of the region which is bounded…

A: