Integrate f(x,y,z) = x+ Vy -z° over the path from (0,0,0) to (3,9,3) given by C,: r(t) =t i+tj, 0sts3 C2: r(t) = 31 + 9j + tk, 0sts3. S (x+vy-2°) ds= D (Type an exact answer.)

Q: Integrate f(x,y,z) = x + √y-2² over the path from (0,0,0) to (4,16,4) given by C₁: r(t)=ti+t²j,…

A: The objective is to integrate the given function f(x,y,z) .

Q: Use the Chain Rule to find Əz/əs and əz/ət. z = x°y', x= s cos(t), y = s sin(t) az as %3D az %3D at

A: Total derivative

Q: Compute Scy dx + xy dy if C goes from (0,0) to (1,2) along the line parameterized as x = t, y = 2t.

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

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

A: Answer

Q: If f(z, v) – 4z°y+ 8zy, then the total differential of f at z-1 and y - 1is: O df - 17 dz + 22 dy O…

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Q: Use the Chain Rule to find dz/ds and dz/dt. z = x°y°, x = s cos(t), y = s sin(t) dz as az at %3D

A: Given:-z=x5y9x=scos⁡t,y=ssin⁡tTo find∂z∂s&∂z∂tBy chain rule∂z∂S=∂z∂x∂x∂s+∂z∂y∂y∂Swe…

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

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Q: dt u = xy + y z tzx x = tcost, y = tsint, z=t at t = a 4

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Q: Find the potential u(x, y) for u +u =0 in the rectangle 0<x< 2 and 0 < y s 2, if the upper side is…

A: The given problem is to solve the potential u(x,y) Laplace partial differential equation, we have to…

Q: Compute for the nonhomogeneous linear DE. d²s ds + dt2 s = 0, dt ds = 0, t = 0 a. 4t + 2cost %3D dt…

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Q: 1. Verify that (t) = et, y(t) = e' satisfies the system %3D dx 3y3 dt dy y, dt %3D

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Q: Use the Chain Rule to find dz/dt. z = cos(x + 7y), x = 5t5, y = 3/t dz dt II

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Use the Chain Rule to find aw at w = xycos z; x = t6, y = t³, z = arccost

A: The given functions are w=xycos z ; x=t6 , y= t3 , z= cos-1t. To Evaluate: ∂w∂t. As per policy, we…

Q: Let w(x, y, z) = x² + y² + z² where x = sin(7t), y = cos(-3t), z = e-4t. dx dy dz dw dt dt' dt dt…

A: Given problem:- wx,y,z=x2+y2+z2,x=sin7t,y=cos-3t,z=e-4t Find dwdt

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

A: Consider the provided question, Hello. Since your question has multiple sub-parts, we will solve…

Q: Evaluate Vf dr where f(x, y, z) = 4xye and C is the path parameterized by r(t) = costi+ sin tj+tant…

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Q: Evaluate f S S 4.x² + 4y² + 4z² dV, where R is the hemisphere centered at the origin, R having…

A: Given that:- ∫∫∫R 4x2+4y2+4z2 dv where R is thehemisphere centered at the origine havingradius 2.…

Q: Use the Chain Rule to find dz/dt. z - x2 + y2 + xy, x = sin(t), y - 2e Use the Chain Rule to find…

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Q: Evaluate the line integral fe y dx + x dy where C is the parameterized path x = , y = f, 3 <iS9.…

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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: Evaluate the line integral f. F. dr where F = (2 sin a,–5 cos y, 10xz) and C is the path given by…

A: We will evaluate the given line integral.

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

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Q: Use the chain rule to find dw/dt, where w=x^5y^4+y^3z^2, x=e^t y=e^tsint, z=e^tcost First the…

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Q: Use the Chain Rule to find dw/dt. In(Vx² + y² + z² ), x = 3 sin(t), y = 5 cos(t), z = 6 tan(t) W =…

A: We have to find the derivative  using chain rule.

Q: the = x + y + 3z dt dy a) = 2y + 3z dt dz = 3z %3D dt 1. Write the linear s Find the eige envalı

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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: Use the Chain Rule to find dz/ds and dz/dt. Z = tan(u/v), u = 3s + 6t, v = 6s - 3t dz ds dz at Need…

A: Given z=tanuv , u=3s+6t , v=6s-3t

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

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: The two functions x(t) and y(t) satisfy the simultaneous equations dx/dt - 2y = -sin(t), dy/dt + 2x…

A: Given: dx/dt - 2y = -sin(t), dy/dt + 2x = 5cos(t)

Q: (b) || 6xy dV, where E lies under the plane z 1+x + y and above the region in the xy-plane bounded…

A: A triple integral involves the integral with respect to x,y, and z. In this problem, we have to…

Q: dz at (u, v) = (1,1) if du Use chain rule to find -z + 1);), = x = 3u – v², y = u® z = x sin( (y? |…

A: If the input of the function is more than one, then it is called a multivariable function. In this…

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

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Q: Use the Chain Rule to find dz/dt. z = x2 + y2 + xy,    x = sin(t),    y = 3et

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Q: If w = x²y - y²z³,x = rCost,y = rSint, dw z = re' , (r = 2)and(t = 0)then dt

A: Given equations - w = x2y-y2z3       ...............(1)x = rcost        ............(2)y = rsint…

Q: Use the Chain Rule to find dz/dt.z = sqt(8+x^2+y^2,    x = 4 ln t,    y = cos t dz/dt=

A: Please refer to the image below

Q: Integrate f(x, y)= y cos xy over the rectangular 0 sxsm, 0 s ys 1*

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Q: Use the Chain Rule to find dz/dt. z = xy9 − x2y,    x = t2 + 1,    y = t2 − 1

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Q: Solve ut = upx in the interval [0, 5] with u(0, t) = 0, and u(5, t) = 1 for t > 0 and u(x, 0) = 0…

A: Hi! As per norms, we will be answering only the first question. If you need an answer to other then…

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

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

A: Consider the given function, Tx,y=100-x2-2y2 the differentiate partially, ∇T=-2x, -4y the slope at…

Q: Use the Chain Rule to find dw/dt. w = In V x2 + y2 + z2 x = 9 sin(t), y = 3 cos(t), z = 5 tan(t) dw…

A:

Q: dy _ у-х dx 1+x y(0) =1 at the point x=0.1

A: Given differential equation is dydx=y-x1+x,y0=1.

Q: Let z = g(x, y) = e² cos y + y ln(x – 1). | Use local linear approximation to estimate g(1.99,…

A: Here, z=g(x,y)=ex cos y+y ln (x-1) is the given function.

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…

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Q: Use the Chain Rule to find dz / dt or dw/ dt.(odd) z = xy3 - x2y, x = t2 + 1, y = t2 -1

A:

Q: Integrate f(x,y,z) = x + √√y-z² over the path from (0,0,0) to (4,16,4) given by C₁: r(t) = ti+t²j,…

A:

Q: dz dt || z = cos(x + 3y), x = 8t³, y = 9/t

A: By the use of chain rule we need to find the required derivative.

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.