Find the Jacobian w/ respect to UVW X=U(3-v), Y= uv(3-w), Z=Uw

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: The gradient of f(x,y,z) = e*+Ysin z + (y + 1)arccOS x at point %3D will be given by DA (e-2, e, 0).…

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Q: Find the linearization L(x, y) of the f(x, y) = x°y® at the point (2, 2). L(x, y) = %3D

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Q: A particle is under the influence of the force F= (-cosh (4x4) + xy)i + (e-y + x)j. The corner…

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Q: Find div F and curl F if F(x,y, z) = xzºi+ 5y°x²j+ 5z?yk.

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Q: Evaluate | (transparent gamma symbol) ∫(x2 + y2) dz | where z = x + iy with (transparent gamma…

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Q: Integrate ƒ(x, y, z) = (x + y + z)/ (x2 + y2 + z2 ) over the path r(t) = t i + t j + t k, 0 <…

A: The equation of the parametric curve (path) is:   Path r(t) = x(t) i + y(t) j + z(t) k   And the…

Q: dz Find using chain rule, where z=, V-,x-e", y-e". dt

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Q: UNIVERSIT b) Given z = f (x – y, 2x – 2y, 3x – 3y). Show that - dz dz + = 0. dy

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Q: Find f-(x, y) and fy(x, y). f(z, y) = (y° tan(5z)) f-(x, y) fy(x, y) =

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Q: Let x (u, v) = u? - v² , y (u, v) = 2 uv. Find the jacobian J (u, v).

A: We have to find the jacobian Ju,v for xu,v=u2-v2 and yu,v=2uv.

Q: tu+v dt In(t) f(u, v) = u-1 fy Find using the chain rule u = x +y³, v= 3y- 3xs

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Q: of the valve matix is consistant e an linear

A: Given augmented matrix is: -412h2-6-3 Let the variables be x, y. The above augmented matrix will…

Q: Solve ux – uy +yu = 0, where u is a function of x and y. %3D

A: Given: ux-uy+yu=0. The objective is to solve u, where u is a function of x and y.

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.

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Q: Let F(x, y, z) =2x2+3y2+4z2. For which unit vector 0 will the directional derivative DoF at…

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Q: Let X, Y be jointly Gaussian, standard, and Cov (X,Y) = y. Find pdf of Z = X +

A: Answer:-  Given that, X and Y have jointly Gaussian distribution.

Q: (a) 3y' In (u) dy

A: We will use the ILATE rule in this example to solve the integral and for solving we use the formula…

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

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Q: he upward flux of

A: Introduction: Let F be a function and let the region is S, then the flux of the function is given…

Q: dz Use chain rule to find at (u, v) = (1, 1) if dv z = z sin(y² – z + 1)4), e = 3u – v², y = vº.

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Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) : 5x sin(xy)…

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Q: The gradient vector for the surface xy + xz + yz = 1 at the point (1, 1,0) is (1, 1,0). Select one:…

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Q: The gradient vector for the surface xy + xz + yz = 1 at the point (1, 1,0) is (1, 1,0). Select one:…

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Q: Evaluate fs xyz dS where S is the triangle with vertices (1,0,0), (0, 2, 0), (0, 1, 1).

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Q: Let x,(t)-v(t)+sin(r), x,-vt) then x,(t)= xN-cosit) Select ones True, False

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Q: Find the directional derivative D,f(P) of f(x, y, z)= cosx+y+z°-5 at P:(, 1, 1) in the direction of…

A: Solved below

Q: Find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at (x,…

A: Let the required path be γt=xti+ytj . Then the velocity vector in the direction of maximum…

Q: Line WY bisects Line UV at Y. If UY = 2x + 1 and YV = x +7, find UV.

A: Meaning of biscsts is dividing into 2 parts .

Q: b) Use chain rule 1 - arctan u, where u = e* y =

A: Given y=1u - arctan u, where u=ex apply derivatives on both sides…

Q: Find the symmetric equations for the normal line LN to the surface S:f (x,y) = 5VT +y? at the point…

A: Given function is S:fx,y=5x2+y2. We have to find the symmetric equation for the normal line LN to…

Q: Use the Chain Rule to find az/ðs and ôz/dt. z = arcsin(x – y), x = s² + t?, y = 2 - 2st as az at II

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Q: Find the Second appoximation for the System. X Sin y at (xo,,)= (1, 1). y=Cosx

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Q: Find the direction derivative of f(x,y)= Xe ² + y ² at the paint (2,1), by the dirction of V = i- j

A: Topic:- application of derivatives

Q: Find the linearization L(z, y) of f at the given point. Surface: f(r, y) 6tan '(ary) (2) Point: 2,…

A: To determine the first order (linear ) approximation to f(x,y) at the given point

Q: Let f(x, y, z) = 3xy + 2yz - xz. Find the directional derivative of f(x, y, z) in the direction of…

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Q: Find up +Uy given that u (x,Y)s. (x,x)s

A: Given that ux, y=tanx3+mx2y2+my4m-x2-y2 To find ux+uy we follow the following steps calculate…

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

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Q: a) If W = F(x ,y),where x =v²-g and y 2vg calculate W +W, %3D b) What is the directional derivative…

A: W=f(x,y) and x= v2-g2 & y=2vg   Wx = dW/dx = (df/dx*dx/dv) + (df/dx*dx/dg) ..............From…

Q: Choose the direction vector for which the function f defined by f(x, y)= sin(3x) cos(11y) has the…

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Q: Find ∂U/∂T and ∂T/∂U when ((TU −V )^2)ln(W−UV) = ln(2) at the point (T,U,V,W) = (1,1,2,4).

A: Given that: TU-V2 ln W-UV=ln 2  We have to find ∂U∂T and ∂T∂U at the point T, U, V, W=1, 1, 2, 4

Q: Find a vector that gives the direction of maximum rate of increase for the e2y cosx at (n/4,0).…

A: Consider a function . Then the maximum rate of change of this function occurs at the direction of…

Q: az and ди az Given that z = exy, x = 2u + v, y = , find (using chain dv rule).

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Q: Let h(r,y) = r'e. Find its linearization at the point (1,0) and use this to approximate f(2,0). %3D

A: Given function is h(x,y)=x2ey we have to find linearization at point (1,0). then to approximate…

Q: Use the Chain Rule to find zz and zy given sin(u) tan(v), u = 3x + y, and v = x – y. %3D

A: Given z = sin(u) tan(v)where u = 3x + yv = x - y

Q: Consider Y; = 0 + 0,X¡ + E¿, i = 1,2,..,n, e, - N(0,0), the cov(ô,Y) = %3D

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Q: Find the Jacobian a(x, y) / a(u, v) for the indicated change of variables. x = eu sin v, y = eu cos…

A: To find the jacobian.

Q: Find the Jacobian a(x, y) / a(u, v) for the indicated change of variables. x = eu sin v, y = eu cos…

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Q: Since we have sin(r +y) sin(r) + sin(y), the function sin(r) is a linear transformation.

A: We know T: V--->W  is said to be linear transformation if, T(x+y)= T(x)+T(y) for all x,y in V…