3-find the gradient of the function v if_w=(xy)/z at the point(1,-2,1), find the directional derivative of w in the direction of vector v = 2i + j - 2k, then find the maximum value of the directional derivative.

Q: Suppose you are climbing a hill whose shape is given by the equation z = 1000 −0.005x2 −0.01y2 where…

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Q: Find the maximum value of the directional derivative at the point (3, 4) of the function f(x) Round…

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Q: obtain the gradient of the function f(x,y,z)=x^2y+5xz

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Q: Consider the function f(x, y, z) = xy+yz² + xz*. Find the gradient of f: • x+z? 2yz +3z²x Find the…

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Q: The temperature at a point (x,y,z) is given by T(x, y, z) = 200e**-y*/4=#"/9, where T is measured in…

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Q: 4 2 IF Ø = 2x2² - xy₁ FIND 01111 AT THE POINT (2-2,1)

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Q: 1. At the point (1, -1), the function (z,y) has a derivative of b in the direction toward (3, 1) and…

A: Given  that at the point (1,−1), the function f(x,y) has a derivative of 5 in the direction toward…

Q: Explain physical meaning of gradient of scalar field. How gradient is different from ordinary…

A: Gradient of a scalar field: The gradient of a scalar quantity is a vector quantity whose magnitude…

Q: gravity and wind.

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Q: Which direction is the directional derivative of the function f (x,y, z) = x2 – 2yz at point…

A: Solution: The function is fx,y,z=x2-2yz The point is P1,1,1 We have to find the direction in which…

Q: Vector A satisfies the vector transformation law, A'=SA. Show directly that its time derivative…

A: Given that a vector A satisfies the vector transformation A'=SA Query is to show that the derivative…

Q: 3. g(x, y) = cos-1 xy, (1,0), v = î + 5ĵ

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Q: Find the unit vectors that are parallel to the tangent of the polynomial y= x^3 +2x + 1 at the point…

A: Consider the given function and differentiate to get the slope of the tangent.

Q: The position vector r describes the path of an object moving in the xy-plane. Position Vector Point…

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Q: The temperature on a cubic box [0, 4] × [0, 4] × [0, 4] (measured in meters) can be described by the…

A: Function, Tx, y, z=x2y+y2z

Q: (3) This problem will walk you through the steps of finding a directional derivative through the…

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Q: Find the gradient of the function whose center is at the origin and radius of 7units…

A: We have to find gradient of the function whose center is at origin and radius of 7 units. We know…

Q: Q4/ Find the directional derivative of the function F(x,y,z)=x+xcosz-ysinz+y at the point P.(2,-1,0)…

A: The given function is; F(x,y,z)=x+xcosz-ysinz+y

Q: Find the directional derivative of f (x, y) = e" /Ty at the point (1,16) in the direction of the…

A: From the given problem:   fx,y=exxy ; p1,16   And the direction of the negative y- axis means :…

Q: Determine the maximum gradient/slope of the function f(z,y) = ² - 32² H at the point (z, y) =…

A: Given that  fx, y = y2x - 3x3                   ∂f∂x = y2 ∂∂x1x -3 ∂∂x x3…