Determine a unit vector in the direction in whichf(x,y) = 4x³ y² increases most rapidly at point P(-1,1).

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: In what direction from the point (1,-1) is the instantaneous rate of change of f(x.y) = 8x* – 10x?y?…

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Q: Consider the curve y = 10 + 4x − x^(2) at (x, y) = (3, 13). Find a vector, v, that has length 4 and…

A: Given the curve y=10+4x-x2 at (x,y)=(3,13).

Q: find the velocity and acceleration vectors in terms ofur and uθ .1. r =θ and dθ/dt = 2

A: Given, r=θ and dθdt=2   Find Velocity and acceleration vectors in terms of ur and uθ:

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 3x sin(xy)…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: Let f(x, y) = 5y² In(4x). Then Duf(1,4) in the direction of the vector (-2,-2) is

A: The explanation of answer as follows

Q: Find the directional derivative of f(r, y, z) = yr + z* at the point (2, 3, 1) in the direction of a…

A: Directional Derivative of a Function of Three Variables =>Directional derivative of  f ( x , y ,…

Q: Find the directional derivative of f(x, y, z) = zy + xª at the point (2, 1, 3) in the direction of a…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Find the velocity and acceleration vectors in terms of u, and ug. r= 6 sin 2t and 0 = 4t v=u, +Due…

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Q: Let F(x,y,z)=3x2+3y2+4z2. For which unit vector 0 will the directional derivative D0F at  (12,12,12)…

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Q: Find the tangential and normal components of acceleration for the position vector denoted by 7 = (t…

A: We have given position vector  t+29,2t,t2 Then, Tangential component of acceleration aT=r't.r''tr't…

Q: Evaluate the directional derivative Duf (3, 4) if ƒ (x,y) = /æ² + y² and u is the unit V vector in…

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Q: Compute the directional derivative of g(x,y)=sin(pi(5x-5y)) at point P(1,-3) in the direction…

A: Firstly, we calculate unit vector in direction of vector u.

Q: Find the velocity vector in terms of u, and ue- T=2 cos 2t and 0= 4t %3D O A. v= (4 sin 2t)u, + (8…

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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: Find the directional derivative of f(x, y, z) (2,1,3) in the direction of a vector making an angle…

A: Given the function f(x,y,z)=zx+y4

Q: Again just working on examples for exam, would like to see how you solve this to see if it is the…

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Q: Find the directional derivative of the function f(r, y) = 1+5x /j at the point (5, 1) %3D in the…

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Q: Find the directional derivative of f at the point (1,2) in the direction of the vector v = = (1, 3).

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Q: A point, p, is moving with acceleration 6t j -k at time t. If at t 1, the coordinates of P are (1,…

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Q: Find the velocity and acceleration vectors in terms of u, and ug- = 5 sin t and 0= 5t = ( 5 cost)u,…

A: Topic:- application of derivatives

Q: Find the directional derivative of f(x,y) = x² + y² – 2x – 4y at the point (-2,3) in the direction…

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Q: It is known that the acceleration vector for a particle is given by A(t) = 4j + 2tk. Determine the…

A: We need to determine vector equation of curve traced.

Q: An eagle rises in a helical path given by the vector function r(t) =〈250cost, 250sint, 100t〉 where r…

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Q: Find the directional derivative of f(x,y,z)=yz+x^4 at the point (1,2,3) in the direction of a vector…

A: According to the given information, it is required to find the directional derivative.

Q: Find the direction in which the maximum rate of change occurs for the function f(z,9)2zsin(ay) at…

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs for…

A: Given: fx,y,z=3x+7yz 1,7,-1 To find: Maximum rate of change of f at the given point. The…

Q: Find the directional derivative of in the direction of the vector (1,3) at the point (-1,2)

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Q: Find the direction in which the maximum rate of change occurs for the functio f(r, y) = 2x sin(ry)…

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Q: Find the directional derivative of the function f(x, y) = 2x2y + 6xy at (1, 1) in the direction of a…

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Q: In what direction from the point (1,-1) is the instantaneous rate of change of 22 f(x,y) = 3x* –…

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Q: Find the directional derivative of f(x, y) = 10 − 3x^2 + (y^4)/4 at P(2, −3) in the direction of the…

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Q: Represent the plane curve by a vector-valued function. x2 + y2 = 25

A: It is given that, x2 + y2 = 25. Let x=5cost and y=sint , Then 5cost2+5sint2=25cos2t+sin2t=25

Q: Find the directional derivative of f(x,y,z)=xe +ye² at (0,0,0) in the direction of the vector…

A: As per our guidelines, I can answer only one question. To know rest please re upload particular…

Q: Find a vector that gives the direction of maximum rate of increase for the 6xyz at (-1,2,1) (a)6(2i…

A: To find A vector that gives the direction of maximum rate of increase.

Q: a) What is the rate of change of f(x, y) = 3xy + y^2  at the point (2, 4) in the direction of vector…

A: (a) Given Data: Function: f(x, y)=3xy+y2 Point: (x, y)=(2, 4) Direction of vector: v=-3i-j The…

Q: Find the directional derivative of f(x,y, z) = yz +x? at the point (3, 2,1) in the direction of a…

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Q: Find the directional derivative of the function f = In (x² + y2) at the point P(4,5) in the…

A: By Bartleby policy I have to solve only first one as Q)3)a) and Q)3)b) are unrelated  problems.These…

Q: The directional derivative of f(x, y, z) = xyz at point (-1, 1, 3) in the direction of vector î - 2ĵ…

A: Remark: We know that the directional gives the rate of change of a function at a specific point in…

Q: The directional derivative of f(x, y) = xe + cosxy at P,(2,0) in the direction of the vector 3i - 4j…

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Q: Let f (x,y,z) = xye² + yze*. From point (1,0,1), which unit vector points in the direction in which…

A: Consider the given information. fx,y,z=xyez+yzex The point is 1,0,1. The direction in which f…

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: (B) At point (1,5), Find the Vector that is tangent and Normal to the curve: X' = 2y + 10

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Q: Find a unit vector pointing in the direction in which the maximum rate of change occurs for the…

A: Consider the formula for vector ? f (x, y) in the direction of the maximum rate of change for the…

Q: Q1. Find the directional derivative of = x²z + 2xy² + yz2 at (1, 2,-1) in the direction of vector…

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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: Calculate the directional derivatives of the function f(x,y) = x² – y? in the direction of the…

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Q: What is the directional derivative of f(x, y) = 4xy+ y cos x at the point (0, 1) in the direction of…

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

A: Dot product of A.B is ad+be+cf where A=<a,b,c> and B=<d,e,f>.