Find the linearization L(x, y) of the function f(x, y) = (x^3)(y^6) at the point (-2, -2).

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

A: We have to find the maximum rate of change

Q: a. What is the gradient at the point (4,0,1)?

A: Consider the given function fx,y,z=x2+y2+2z2+3.  The gradient of a function is given by,…

Q: Find the gradient of the function at the given point. In(x2 - Y) - 9, (3, 8) Vz(3, 8) =

A:

Q: x = X, +(-

A: let the initial velocity be v0 , and the initial distance be x0 .and in time t , the new velocity…

Q: How do you compute the gradient of the functions ƒ(x, y) and ƒ(x, y, z)?

A: Given, The function f(x,y). It's gradient is given by, For example,

Q: Tangent to the curve z2 = 2xy + x2 , z = 3 , at the point ( 1, 4, 3) %3|

A: For a surface of the form: f(x, y, z)=0, the equation of the tangent at x0, y0, z0 is defined as…

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

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Q: What is the maximum slope of f(x,y,z)=ye^x-x^2sin(z) at the point (0,7,-3)?

A: Given the function fx,y,z=yex-x2sinz and the point 0,7,-3. Computing the partial derivatives,…

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: Find the gradient of the function at the given point. In(x² – y) – 8, (3, 8) Vz(3, 8) =

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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 the gradient of the function at the given point. Function Point f(x, у, 2) 3 x2 + y2 + z2 (7,…

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

A: Gradient of a function f(x,y,z) is given by,          grad(f(x,y,z))=i∂∂x+j∂∂y+k∂∂zf(x,y,z)…

Q: c. y = 2Vx when x = -1 с.

A: We have to find the gradient

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

A: Given:        fx,y=4yx   at point 4,5     The rate of change of f is     ∇fx,y=∂f∂x,∂f∂y…

Q: Find the gradient of the ellipse 2x2 + 3y2 = 14 at the points where x = 1

A: It is given that the equation of an ellipse is ;  2x2+3y2 = 14 We have to find the gradient of the…

Q: The gradient vector of the function f(x, y) = cos(4x - 6y) is (4 sin(4x - 6y), -6 sin(4x - 6y)).…

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Q: Find the orthogonal trajectories of the family of circles with center at the point (0, 1) and radius…

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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 direction of maximum decrease of the function f(x, y, z) =exyz at the point P(1,1,1) and…

A: Given function is

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

A: The given function is: f(x,y)=8yx

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

A: The objective is to find the maximum rate of change of f at the given point and the direction in…

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: 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 gradient of the function at the given point. In(x - y)- 4, (3, 8) Z = Vz(3, 8) =

A: The objective is to find the gradient function at the given point.

Q: w = 3x² – 5y² + 2z², (1,1, –2)

A:

Q: Find the directional derivative of f(x, y, z) = xy²z³ at P(3, 1, 1) in the direction of Q(0, -5, 7).…

A: Given function: fx,y,z=xy2z3

Q: Find the gradient of w= 3x² - 5y* + 2z at the point (1, 1, -2)

A: The given function is: w=3x2-5y2+2z2

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

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Q: First, compute the gradient of the function p(x,y)= 12- 2x-y Then evaluate it at the point (- 1,2).

A: We need to find partial derivatives with respect to x and y to find gradient

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

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Q: Tangent to the curve z2 2xy + x² , z = 3 , at the point ( 1, 4 , 3 )

A: Consider the curve, z2=2xy+x2 ⇒x2+2xy-z2=0

Q: Find the gradient of the function f(x, y) = 7x2 + 6y, at the point (-2, 6). [ i.e., find V f(-2,6) ]

A: As we know that the expression of the gradient of the function is: ∇fx,y=i∂∂x+j∂∂yfx,y Given:…

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. In(x2 - у) - 3, (2, э) Vz(2, 3) = %3D

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Q: A bee was flying upward along the curve that is the intersection of z = x⁴+xy³+12 with the plane…

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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: determine the gradient and equationof the tangent to the curver f(x,y) = 0 in the point (a,b) for…

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Q: Find the critical points of the function by using algebraic techniques (completing the square) or by…

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Q: Line has a -intercept at (0, 3) and an -intercept at (4, 0), . what is the gradient of L

A: The line has y-intercept at 0,3, and x-intercept at 4,0. Thus, the gradient of the line will be…

Q: Tangent to the curve z2 = 2xy + x² , z = 3 , at the point ( 1, 4 , 3

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Q: Compute the gradient for the function f (x, y) = 4x² – 9y at the point (10, -9) %3D

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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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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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