Let F(x,y, z) = rye" – 2² Jī and P(1,0, –1).

Q: Suppose that over a certain region of space the electrical potential V is given by V (x,y,z) = 3.x²…

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Q: Find the point on the graph of z = 3x2 + 2y at which vector (24, 8, 2) is normal to the tangent…

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Q: 10) Find a unit vector in the direction that f (x, y, z)= 2x² +6xy² – xz' increases most rapidly at…

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Q: Find the derivative of the vector function r(t) = ta x (b+tc), where а 3 (—3, —4, — 2), b — (—2, —5,…

A: Topic:- vector and it's derivatives

Q: Find the gradient vector field of f(x, y, z) = 9x5 + 7y3 + 6z?

A: To find the gradient of  f(x,y,z)=9x⁵+7y³+6z²

Q: determine the unit vector from which f grows faster in P and determine a rate of change of f in P in…

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Q: Suppose you are given a vector-valued function modelling the velocity of a particle in space. At…

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Q: determine the unit vector of the direction from which f grows fastest in P and determine the rate of…

A: Here I am attaching image so that you understand each and every step.

Q: Find the gradient vector field of f(x, y) = ln(5x + y)

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Q: Let f : R+ × R → R be the function f(x,y) = 2x + VTy³. (a) Find a tangent vector to the graph of…

A: The given function is: fx,y=2x+xy3 The given point is: 1,1,3

Q: Find the gradient vector field of f(x, y, z) = 9x² + 8y* + 6z3

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Q: Find the gradient vector field of f(r, y) = In(x + 3y)

A: Solve for the gradient vector

Q: Let f(x, y) = x²y'. At the point (-1, 2), find a vector (a) In the direction of maximum rate of…

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Q: (d) Find a vector function that represents the curve of intersection of the two surfaces: the xy…

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Q: Suppose given a function f(x, y, 2) of three variables, and a point (o, y0, 20) €R. Explain in your…

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Q: ..Find the Gradient Vector Field for: f (x,y, z) = x²ye/z

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Q: Let f (x, y) = x 4y-2 and P = (2, 1). Find the unit vector that points in the direction of maximum…

A: Concept: The Unit vector is a quantity which has a magnitude as 1and as well as direction, it is…

Q: Find the increase rate of the scalar V at point P from origin to the point P(2,6; 9,8 ; 9,5) where…

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

Q: Find the linear approximation to f(x, y, z) = at the point (–2, 3, 2) f(x, Y, z) ×

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Q: Determine the rate of change at (0, 2) of the function 1 h (x, y) V1+x² + 2y² in the direction of…

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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: Find the gradient vector field Vf of f. 1 f(r, y) = (y – 2)?

A: For a given vector fx, y the gradient vector denoted by ∇f is ∂ ∂ xf∂ ∂ yfSo,=∂ ∂ x12y-x2∂ ∂…

Q: Find the gradient vector field of f(x, y) = tan(2x − 3y).

A: Given fx,y =tan2x-3y         we find the gradient vector of fx,y

Q: Find one normal vector of the tangent plane to f(x, y) = cos(x² +y²) at point P(1,1, cos 2).

A: As we know the expression of the normal vector to the tangent plane at a point on the curve can be…

Q: Find the gradient vector field of f(x, y, z) 5x+ 2y+8z

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Q: Find the point on the graph of z = 3x2 + y at which vector n = (24, 2, –1) is normal to the tangent…

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Q: Find the gradient of f(x, y, z) =e^y cos(xz) at (1,0,1) .

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Q: Find the linear approximation to f(x, y, z) = " at the point (2, -1,1): f(x, y, z) z

A: Given the function

Q: Find the derivative of the vector function r(t) = ta x (b+tc), where (5,-4, 1), b = {(-4, –3,1), and…

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Q: Find a unit normal vector to the surface f(x, y, z) = 0 at the point P(2, - 3, 11) for the function…

A: The unit vector normal to the surface f(x, y, z)=0 is ∇f∇f. where ∇f = fx, fy, fz and ∇f = fx2 + fy2…

Q: Find the gradient vector field of f(x, y) = ln(4x + 2y)

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Q: Suppose that over a certain region of space the electrical potential V is given by V(x, y, z) = x^2…

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Q: ind a unit vector in the direction in which fincreases most rapidly at P, and find the rate of…

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Q: Find the gradient vector field of f (x, y) = y sin(xy).

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Q: Find a unit vector in the direction in which f(x, y) = 6 cos(x – 5y) decreases most rapidly at P and…

A: Given, fx,y=6cosx-5y Find the unit vector and rate of change of f at P.

Q: The position of a particle moving in the xy-plane is given by the vector (4t, y(2t)), where y is a…

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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: (b) Identify the unit vector u pointing in the direction of maximum increase of the function f(x, y)…

A: Find your answer below

Q: Find the linear approximation to f(x, y, z) = " at the point (2, –1, 1): f(x, y, z) =

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: Find the gradient vector field of f(x, y) = In(2x + 3y) V

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Q: Find the a unit vector in the direction of which f(x, y) = In (1 + xy) increases the most rapidly at…

A: Consider the given function as fx,y=ln1+xy

Q: Let f(x, y, z) = x² – y? + 2z. Compute the rate of change of f in the direction of the vector (v2,…

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Q: Suppose a vector function F(x, y) = 3xi + 2xyj + y ln zk moves along a path C where x = t2, y = t +…

A: The formula to find the work done by the vector function helps to find the required work done. The…

Q: Suppose that over a certain region of space the electrical potential V is given by V (x, y, z) = 6x²…

A: We have to find the rate of change of V at point P in direction of v .

Q: Find the gradient vector field of f(x, y, z) = e® 5x+2y+8z

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Q: find the velocity and acceleration vectors in terms ofur and uθ . r = a(1 + sin t) and θ = 1 - e-t

A: The velocity and acceleration in terms of ur→ and uθ→ are given by: v→=r'ur→+r θ'uθ→a→=r''-r…

Q: The temperature T, at a point (x, y) in the xy-plane is given by T(x, y) = 4x^2y^3 degrees Celsius.…

A: We have to find a unit vector in the direction in which the temperaturedecreases most rapidly at (2,…

Q: Find the derivative of the vector function r(t) = ta x (b + tc), where a = (2,-2, 5), b (2,-5, 3),…

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Q: f(x , y) = e* sin( y) at P= (1, T/4) with u =(-1N5, 2N5 ).

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Q: Find the gradient vector field of f(x, y, z) = e9z+6y+7z V

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