The temperature at the point (x, y) on a metal plate is  T(x, y) = x/((x^2)+(y^2)). Find the direction of greatest increase in heat from the point (1, 2).

Q: What is the gradient vector of a differentiable function ƒ(x, y)? How is it related to the…

A: The objective is to write what is the gradient vector of a differentiable function ƒ(x, y) and how…

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A: we need to find gradient of given surface to know about direction of normal vector to tangent plane

Q: 25 at the point ( 1, -1, 2 ).

A: Given that : The surface  8x2+y2+4z2 = 25 , point = ( 1, -1, 2 ).

Q: A heat-seeking particle is located at the point (2, −3) on a metal plate whose temperature at (x, y)…

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Q: the equation of the tangent plane where z=x^2 - 2xy - y^2 -8x + 4y

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A: In trapezoidal rule the value of a interval is computed by ∆x=b-an. In the above formula a is the…

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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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Q: Calculate the instantaneous rate of change of g at the point (4, 1,2) in the direction of the vector…

A: Instantaneous rate of change of a function g in the direction of a vector v is  =∇g.vv Maximum rate…

Q: Find the direction 0 in which the directional derivative of the function x + y f(x, y) = 2(x + y) -…

A: Given that: f(x, y)=2(x+y)-x+yxy

Q: Find the maximum rate of change of f(x, y, z) = x + y/z at the point (-3, -1, 3) and the direction…

A: As per honor code, we are entitled to solve only one question at a time so I am providing the same.…

Q: wn is bounded by the line y = − 5x + 4, - -axis and the y-axis. y X

A: we will find the area.

Q: Integrate ƒ(x, y, z) = x - 3y2 + z over the line segment C joining the origin to the point (1, 1, 1)

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Q: Find an equation of the tangent plane to the surface 9x2 + y2 + 4z2 = 25, at the given point (0, −3,…

A: Concept: The two expressions connected by equal to be called an equation. The expression on the two…

Q: Find the maximum rate of change of f(x,y, z) = r + y/z at the point (-1, -3, 5) and the direction in…

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Q: What is the gradient vector of a differentiable function ƒ(x, y)? How is it related to the…

A: Consider the function f(x,y), the gradient vector of a differentiable function f(x,y) is…

Q: Find the minimum rate of change at (2,-2,0) and it's direction for f(x, y, z)= =. zy² I in the…

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Q: Consider a closed rectangular box with dimensions xx  ft by  yy  ft by zz ft. If xx  is increasing…

A: Proceed as shown

Q: . Find the directional derivative of y fx, у, 2) x+ z at P(2, 1, – 1) in the direction from P to…

A: NOTE: Refresh your page if you can't see any equations. . the given direction is P to Q find the…

Q: Find the gradient of the function at the given point. Function Point (7,4) f(x, y) = Vf(7, 4) = x +…

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Q: Find the maximum rate of change of f(x, y) = ln(x² + y²) at the point (3, 5) and the direction in…

A: Here is the solution of the given problem. Unit Direction:

Q: Find the maximum rate of change of f(a, y, z) tan(6z + 4y + 2z) at the point (- 4, 3, - 6).

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Q: Suppose that f(æ, y) f(x, y) in the directional (1, – 1) and at the point = xy. The directional…

A: Here, the given function is: f(x,y)=xy So, ∇f=∂f∂x,∂f∂y⇒∇f=y,x⇒∇f(4,-3)=-3,4

Q: Determine the directional derivative of X²Yz +4XZ² at the point P(1,-2,1) in direction a=2û - j +² R…

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Q: Suppose that f(r, y) the point (r, y) 3 (6, ry. The directional.derivative of f(z, y) in the…

A: Given:  fx, y=xy To Find:  To find the direction derivative of fx, y at the point x, y=6, -4, in the…

Q: Find the minimum rate of change at (2,-2,0) and it's direction for f(x, y, z)= =. zy² H in the…

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Q: A airplane is flying horiZontally due north at 200 miles per hODE when it encounters a horizontal…

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Q: 3. At point (1,0,3) on the surface f(x,y) = 2x^2 + 3 y^2+ z^2-11, the directional derivative in the…

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Q: Find the maximum rate of change of f(x, y) = ln(x² + y²) at the point (-4, -4) and the direction in…

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

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A: Given: f(x,y)=ln(x2+y2) at point (-4,-3) to find: maximum rate of change

Q: What is the moment of inertia about the x-axis bounded by the curves y² = -16(x-4), the line 8x-15y…

A: here we have to find the moment of inertia about x axis so we can use integration to find this.

Q: First, compute the gradient of the function f(x,y) = 4+5x²-3y². Then evaluate it at the point…

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Q: Find the maximum rate of change of f(x, y) = ln(x² + y²) at the point (5, 2) and the direction in…

A: As per bartleby guidelines, for more than one questions only 1st one is to be answered. Please…

Q: Find the directional derivative of F(x,y,z)=x3y+4y2z+3xz3 at the point (3,-1,2)   in the direction…

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Q: Find the maximum rate of change of f(x, y) = In(x² + y²) at the point (1, -4) and the direction in…

A: Here, the given function is: f(x,y)=ln(x2+y2)

Q: Estimate the length of the curve y=0.5x² over [1,4] using n=6 and trapezoidal method. Also determine…

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Q: Determine the gradient of the curve 3xy + y² = -2 at the point (1, -2)

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Q: The 50 g bullet travelling at 100 ms-1 strikes the 2 kg block centrally and is embedded within it.…

A: Please check step 2 for the solution.

Q: Find the gradient of the function at the given point. Function Point f(x, у, 2) + y2 + z2 (3, 7, 2)…

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Q: Find the maximum rate of change of f(x, y) = In(x² + y²) at the point (3, 5) and the direction in…

A: This is a problem related to the derivative of the function. For calculating the maximum rate of…

Q: Find the directional derivative of ø = x² + y² + z² at point (1, 2, 1) for a direction determined by…

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Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) 5x sin(xy) at…

A: We have to find the direction in which the maximum rate of change occurs for the function…

Q: Find the length of curve along y = x² from (0,0) into (2,4).

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Q: Find the gradient of the function at the given point. Function Point (8,4) f(x, y) Vf(8, 4) = = = x…

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

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