if x=u(1-v),y=(uv) then verify that a(u,v) a(x,y). =1 a(x,y)'a(u,v)

Q: Calculate the double integral. 6x/1+xy dA, R=[0,6]x[0,1]

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Q: Compute div F, where F(x, y, z) = (x² + 3y, y? – 4z, sin r cos y – 22). A. (4 – sin r sin y, – cos r…

A: Given : F(x, y, z)=(x²  + 3y ,  y² -4z ,  sin(x )cos(y) - z2 )  Now we find div F = ?

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

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Q: 2. Given that f(t) = f cos x cos(t − x) dx, fin integral.

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Q: 2. When object P, with mass m, , moves at v, and object Q, with mass m,, moves at v,, the velocity…

A: Given,For P, mass = m1  and velocity = v1Let, velocity after collision is u1For Q,mass = m2 and…

Q: 10. What is the work done moving a particle from x = 0 to x = 1 m if the force acting on it is F =…

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Q: Two functions u and r of x and y are said to satisfy the Cauchy- Riemann equations if u, = v, and u,…

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

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Q: polar integral rIn 2 V(In 2)²–y² x dx dy c) dx dy

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Q: 4-x? Change the order of integration | | f(x, y, z)dzdydx in the order dydxdz.

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Q: Let u = exsin(y), where x = -(1/2)ln(t) and y = (pi)(t). Find du/dt when x = ln(2) and y = (pi/4)

A: Question is solved.

Q: What is the integrating factor of (1 + cos z) y' = sin z (sin z + sin rcoSI y) - CSC I sin z O1 +…

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Q: 70. Solid bounded above by x² + y² + z² = 36 and below by = 2 Vx + y?

A: Given: Consider The volume of any solid E in R3

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: Provide an appropriate response. If xy + x = 12 and dx/dt = -3, then what is dy/dt when x = 2 and y…

A: We will find the value of dy/dt with the help of the given data x=2 ,y=5 and dX/dt=-3 as following.

Q: bounded by Y=x3, V=1x i rotare about X=1

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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: Use the Chain Rule to find dz/dt. z = sqrt 3+ x^2+y^2, x= 3 ln t, y= cos t

A: Use chain rule to differentiate z

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: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=0,…

A: I am going to solve the given problem by uisng some simple calculus to get the required result.

Q: 4. Curl of f (x, Y, z) = 2xyi + (x² + z²)j + 2zyk is

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Q: integral t 3 et dt

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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: Show that+ = 0, %3D ax dy? where f(x, y) = In(x² + y²) + tan¯'(²) %3D

A: The partial derivative of a two variable function fx,y with respect 'x' can be calculated by…

Q: ]If x' +y +z =9, dx/dt 5, and dy/dt 4, find dz/dt when (x, y,z)=(2,2,1).

A: Topic- application of derivatives

Q: u,v) = ve*tv, and z(u,v) = (u+v)cos v?. OG nd and by using multivariable Chain Rule method. du u=1

A: Given: Gx, y, z=e2x+y+3zxu, v=u lnu+vyu, v=veu+vzu, v=u+v cos v2  To Find: To find  ∂G∂uu=1v=0  and…

Q: Evaluate triple integral ſ´, S,2 ¯* dz dx dy .

A: We can solve this as follows:

Q: Double integrate under z=xy, above the triangle with vertices (0,1),(0,4),(1,1).

A: We have to find the volume by double integration

Q: sin(t) et, X2 sin(t)- cos (t) and X3 D sin(t) + cos (t)] 0. Given that X, cos(t) sin(t) + cos (t)|…

A: The problem is wrong, three vectors are not linearly independent.

Q: Find the total differential. z = 10x6y7 dz = %3D

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Q: 2. Prove that the directional derivative of f(x, y, 2) = ry sin z at (1,2, ) in the direction v = i+…

A: Given:        fx,y,z=xy sinz         x,y,z=1,2,π2    direction v=i+2j+2k   Differentiate the…

Q: Find the total differential of z= f(x, y), where f(x, y) = In Use * for multiplication of variables,…

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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: Let f(x, y) = xcosy - ye*y. fry at (1,0)is equal to: -1

A: See the attachment

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: Find aw in terms u and v if du w= In(x2+y2 +z²), x = ue" sin u, y = ue' cos u, z = ue"; (u, v) =…

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Q: What is the value of the line integral ∫AB xy dx defined by the line y = x +2 and it is along the…

A: The given problem is to evaluate the line integral along the path y=x+2 from points A(0,2) and…

Q: Find the divergence of F(x, y, z) =(a -1 Y, y? + 1' 3xz2 + 2y ) at (2,0, – x COS

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Q: Evaluate the iterated integral. rIn(x) xe-Y dy dx dz 4z 434 3

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Q: Assume that a body moving with velocity v encounters resistance of the form dv/dt = -kv3/2. Show…

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Q: Find the total differential. z = x cos(y) -y cos(x) dz %3D

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: integrate t dt/(1-ct) where c = const.

A: Solved below

Q: Let f(x,y, z) = In(x²2+ z) + y²e*z – cos(2yz). Find fzyx·

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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 local extrema with (binding) g = 0.

A: To determine the extrema of the function f(x, y, z) subjected to the constraints g(x,y,z)=0 Write…

Q: 3. A particle is located at a distance x meters from the origin, a force of x +2 newtoms is acting…

A: To find the work done

Q: ( b). Je2cos (πx) dx .

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

A: Given equation is s=x2+y2. Compute the derivative of s with respect to t.…

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.