Suppose that the temperature at point (x,y, z) in space with the distance measured in kilometers is T(x,y,z)= 10 + x'y + xz' + yz (in degrees Celsius). a.) Find the change in temperature in the direction of v = i + 2j -2k at P(3,5, 4). b.) In which direction does 'T' change most rapidly at point 'P' c.) What is the maximum rate of change at 'P'?

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A: Given that  u=2(1+t)  To find the local acceleration in the x direction of flow

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A: Given fx,y=lnx3y6     at (4, 3) The linear approximation in 2 variables is given by Lx, y=fa,…

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…

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Q: 6. Find the unit vector for which the directional derivative Duf(x,y) of f(x,y) = %3D 3x2 + 4y2 at…

A:

Q: F(X, y,z) = 2x -y? +z?

A: F(x,y,z)= 2x-y^2-z^2 at point (4,-4,2) df/dx= 2 df/dy=-2y df/dz= -2z

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A: According to question given that The origin to the point P(2,6 ;9,8 ; 9,5) where V=3, 3xy+ 2, 6xyz

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A:

Q: What is the linearization L(x, y) of a function f (x, y) at a point (a, b)? How is L(x, y) connected…

A: Linearization L(x,y) of a function f(x,y) is given by the formula

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Q: Determine the local linear approx imation of flx,4,z) =(1+x) (l-y³) (l-2)²' at the point CT, 2,3)

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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,…

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A:

Q: In(3x² – 2y + 4z³); x = t², y = t³ , z =t-l. Find the maximum derivative the function f(x, y) = x² –…

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Q: 5. Compute the directional derivative and gradient of f(x,y,z) = 4x – y²e3xz at (2. –1.0) in the…

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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…

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Q: Let y 4x + 3x + 4. If Ax 0.3 at a = 3, use linear approximation to estimate A %3D Ay =

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Q: The velocity field for a flow is given by V = ut + vj + wk where u = 3x, y = -2y and w = 2z. Find…

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Q: Find the unit vector u along which the rate of change of the function f(x, y) = x 2 + xy3 at the…

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Q: A heat-seeking particle is located at the point (2, −2) on a metal plate whose temperature at (x,y)…

A:

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

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Q: Suppose T(x, y, z) is the temperature at position (x, y, z) and suppose u is a unit vector pointing…

A:

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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,…

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Q: Let f ( x , y ) = 2 x − y + x2 + y4. Which (unit) direction vector u  MINIMIZES the directional…

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Q: Compute the directional derivative and gradient of at (2,-1,0) in the direction of the unit vector…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.