a²+y² » (x, y) # (0, 0) f(x, y) : 0, (х, у) — (0,0).

Q: The gradient of f(x,y,z) = e*+Ysin z + (y + 1)arccOS x at point %3D will be given by DA (e-2, e, 0).…

A:

Q: What is the rate of increase of the scalar function f(x,y,z) = sin (πx/3) sin (πy/2) e^-2z from the…

A: What is the rate of increase of the scalar function f(x,y,z) = sin (πx/3) sin (πy/2) e^-2z from the…

Q: find the directional derivative of f at p in the direction of B.  if f(x,y,z)=x+ycos(z) where p…

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Q: Let x and y be differentiable functions of t, and lets = √(x2 + y2) be the distance between the…

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Q: Find the maximum rate of change of f(x,y)= e^x^2 at (3,0) and the direction in which it occurs.

A: GIVEN DATA : Function fx,y=ex2        TO FIND : Maximum rate of change at 3,0 and the direction  The…

Q: of of Find and for the furction f(xy,z) = x y+ y + xỉ ôx 'ay

A: For the function f( x, y, z ) = x2y + y2 + xz2 . We need to find some partial derivatives.

Q: Bounded by the cylinder x 2 + y 2 = 1 and the planes y= z x =0 z= 0 in the first octant

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Q: a) Find the directional derivative of f(x, y, z) = x²yz + 4xz² at (1, -2, 1) in the direction 2i - j…

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Q: Choose the gradient of the function f defined by f(x,v,z) = cos(xy +9xz + 13yz). O sin(xy O -cos(…

A: Take gradient and solve

Q: Find the directional derivative of the function f(x, y, z) = ryz in the direction normal to the…

A: We havefx,y,z=xyz

Q: Let x and y be differentiable functions of t and lets = sqrt(x2 + y2) be the distance between the…

A: Given that, s=x2+y2

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 derivative of the function at Po in the direction of the vector AC. f(x, y, z) = x² + 2y²…

A: To find the directional derivative of the given function.

Q: Find the directional derivative of f(x, y, z) = cz+y² at (1, 0, 4) in the direction of a =. = IZ

A: Differential equations are those equations of mathematics that involve dependent variables ,…

Q: How is the linearization of f(x, y) centered at (a, b) defined?

A: To define linearization of a function f(x,y) at point (a,b).

Q: . The solid bounded by z = 1 – x², z = 5 – 2x², y = 0, and y – z = 6. |

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

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: How will the contour maps of f (x, y) = x and g(x, y) = 2x with contour interval 1 look different?

A: To describe how the contour maps of f(x, y) = x and g(x, y) = 2x with contour interval 1 look…

Q: find the gradient of function f [x, y,z] = 3x² -y?_z? at paint {i,-Ź, -¡}

A: The given function is fx,y,z=3x2-y3-z2 and the given point is 1,-2,-1. The gradient of the function…

Q: The gradient of f(x, y) = xy at (x, y) = ( – 3, – 2) is %3D

A:

Q: The gradient of f(x, y) = xy at (x, y) = (2, 3) is

A:

Q: continuous function h(x),

A: Differential equation

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

A:

Q: The gradient of f(x, y) = e³ ² sin(3 - y) at (x, y) = ( - 1, – 3) is defined as followed: V f(а, у)…

A: It is gradient vector by using partial derivative

Q: The coordinates of a particle in the metric xy-plane are differentiable functions of time t with…

A: The distance of a point (x,y) and the origin is calculated by d=x2+y2 Given rate of change is,…

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

A: According to the given information, it is required to find the maximum rate of change of f at the…

Q: Determine the set of points at which the function xyz f(x, y, z) 4x2 + 5y2 - is continuous. 1. { }…

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Q: Calculate the directional derivative of the function f(x.y.z)= In(xy+xz+yz) at (1, 1, 1) in the…

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Q: Plot the function f(x, y) = x² – y² over the square region bounded by the lines y =x - 2, y =x+ 2, y…

A: Given the function fx,y=x2-y2

Q: Dete‎rmine if f (x, y) = ={(xsi‎n3y)/(x‎2+y6), (x, ‎y) ≠ (0, ‎0) ={1, (x, y) = (0, 0) is‎…

A: Solution: A graph for a function that's smooth without any holes, jumps, or asymptotes is called…

Q: Integrate f(x,y,z) = x-3y + z over the line segment joining the points (0,0,0) and (2,2,2). %3D

A: Here, we need to integrate f(x, y, z)=x-3y2+z over the line segment joining the points (0, 0, 0) to…

Q: Find the directional derivative of the function at the point in the direction given. f (x, y, z) =…

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Q: |(y) + (0,0) (x. y) (0,0) Show that the function f (x, y). is continuous at the origin however =…

A: consider the equation  f(x,y)=∑xyx2-y2x2+y2 ,0  x,y  #(0,0)xyx2+y2 where f(0,0)

Q: Find normal line and parallel plane to the function f(x, y, z)=√xyz - 4 At point (1,2,8).

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Q: Suppose that f(z, y) = z*y°. The directional derivative of f(1, y) in the directional ( – 1, – 2)…

A: We can solve this as follows:

Q: Let f(x, y) = xe". What is the maximum rate of change of f at the point (2,0)?

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Q: What is the gradient of f(x, y, z) = x³z2 + y³z +125z - 1 at P(5,5,-1) ?

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Q: The maximum directional derivative of f (x, y, z) = x² sin(zy) – yx + 10 | at (-1, 2, 0) is

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Q: Find the gradient of the function and the maximum value of the directional derivative at the point…

A: The solution is given as

Q: How do you find the extrema of a continuous function ƒ(x, y) on a closed bounded region of the…

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Q: The gradient of f(x, y) = ry at (x, y) = (3, 1) is %3D

A: Explanation and solutions is given below....

Q: The gradient of f(x, y) = xy at (x, y) = (3, 3) is

A: Given problem:- Find the gradient of f(x, y) =xy at (x, y) =(3, -3)

Q: What is the rate of increase of the scalar function f(x,y,z) = sin (πx/3) sin (πy/2) e^-2z from the…

A: See the attachment

Q: Find the first partlal derivatives with respect to x, y, and z. f(x, y, z) = 4x²y – 6xyz + 9yz? %3D…

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Q: Compute the gradient of f (x, y) = (x + 2) + xysin(y) at (0, 1)

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Q: /alue of divergence of function (x2y2)î - (z³y – 4x) ĵ + 4y2 xk at (1, 2, 1) is

A: Let f = (x2y2)i^ - (z3y-4x)j^ + 4y2xk^

Q: Let x and y be differentiable functions of t, and lets = √(x2 + y2) be the distance between the…

A: Given equation is s=x2+y2. Compute the derivative of s with respect to t.…