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Q: 4. If A is the point with coordinates (1, 4). B is the point with coordinates (7, 22). Find the…

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Q: 3. Find the gradient of U = 4xz² + 3yz. А. 4z3а, + 3za, + (8xz + Зу)а, В. 4z? а, + 3zay + (8xz +…

A: For a vector valued function U≡Ux,y,z, its gradient is defined as gradU=∂U∂xax+∂U∂yay+∂U∂zaz…

Q: Let = (3, 4, 12) . Find the directional derivative of f(z, y, 2) =1– y² +32³ in the direction of v.

A: Consider the given function, fx,y,z=x-y2+3z3 and v=3,4,12 Now, find the derivative of the function…

Q: Find the directional derivative of the function at the given point in the direction of vector v.…

A: The objective of the question is evaluate the directional derivative at the given point and…

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: Your friends correctly calculate the gradient vector for f(x, y)=x²+y at the point (2,-3) as…

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Q: If f(x, y, z) = 4zy", then the gradient at the point (5, 4, 5) is V f(5, 4, 5) =

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

Q: Explain Directional Derivatives and Gradient Vectors

A: Directional derivative is the rate of a change of a function f at a point (x,y,z) in the direction…

Q: (6) calculate the inrtantanco us rate of at point (4,1,2) in the change of 9 direction of the vector…

A: This is a question of multivariable calculus, the calculus of several variables.

Q: Find the directional derivative of f(x, y, z) = z3 – x²y at the point (5, -2, -2) in the direction…

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Q: Find the directional derivative of f(x,y)=yln(x+y) at the point (-3,5) in the direction of the…

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Q: Find the gradient of the function at the given point. w = x tan(y + z), (13, 7, -5) Vw(13, 7, -5) =

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Q: Calculate the gradient vector Vf of the function f(x, y) = x² – x + y- x²y – 2y2 at the point (2,1)…

A: According to the given information, it is required to determine the gradient vector of the given…

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: An object moves with velocity vector (t,t?,-t) starting at (1,2,3) when t=0. Find the function r…

A: Since you have asked multiple questions so as per guidelines we will solve the first question for…

Q: Find the gradient of the function at the given point. w = x tan(y + 2), (19, 9, -2) Vw(19, 9, -2) =…

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Q: 2. Find the gradient vector at the indicated point f(x, у, 2) 3 ху — In (2),. (2, -2,2)

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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: The level curves of the surface z =x +y are circles in the xy-plane centered at the origin. Without…

A: Consider the given surface. z=x2+y2 The objective of the problem is to find the direction of the…

Q: Find the gradient Vf and the directional derivative at the point P (1,–1,2) in the direction a =…

A: The given function f(x, y, z) = x3z - yx2 + z2.The gradient of a function f is defined as∇f(x, y, z)…

Q: Find the gradient of the function at the given point. In(x? - y) - 3, (2, 3) Vz(2, 3) -

A: We have to find the gradient of the function z = lnx2-yx-3 at the point 2, 3.

Q: Interpret the magnitude of the gradient vector at a point.

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Q: 4. Prove that the vector given by (2xy -y')7+(2x²y-3xy² +2) 7 is a gradient. Also, find the function…

A: The solution are next step

Q: The gradient vector of the function f(x, y, z) = ln(yz) + x² is: Select one: (2x, /, // ) (2x, -, -…

A: gradf =∇f =i∂∂x+j∂∂y+k∂∂zf .

Q: Given the function z = f(x, y) = 3x² +6xy + y² + 8y, find the following: a) Find gradient at (-2, 3)…

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Q: Find the gradient of the function at the given point. In(x2 - y) - 2, Z = (2, 3) Vz(2, 3) Need Help?…

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Q: Sketch the gradient vector ∇f (4, 6) for the function f whose level curves are shown. Explain how…

A: To draw the gradient vector at a point, determine the direction and the length of the vector. The…

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 gradient function for: 21y-

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Q: (х,у,2) xIny + ylnz + zlnx

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Q: Find the gradient of the function at the given point. w = x tan(y + z), (20, 8, -4) Vw(20, 8, -4) =

A: The expression for the gradient vector is:…

Q: Consider the level curves for F (x, y) = x² – y². y (a) How do we sketch in the gradient vectors?…

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Q: According to the function in image 1.1, we can say that its gradient vector at point (1,1,2) is (in…

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Q: Consider the function f (2)= +-z Which direction is a descent direction at z (1,1)?

A: This is a problem of vector calculus.

Q: If f(x,y) = ln(xy) + x^2y^2, how do I calculate the second directional derivative of f in the…

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Q: Find the gradient of the function at the given point. w = x tan(y + z), (10, 5, -2) 2, Vw(10, 5, -2)…

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Q: Find the gradient of the curve y = 36 (2х - 3) at the point (3, 4)

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Q: Find the gradient of the function f​(x,y)=5y−9x at the point (4,4). Then sketch the gradient and the…

A: Given the function

Q: Find the gradient of the function at the given point. w = x tan(y + z), (10, 5, -2) Vw(10, 5, -2) =

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

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Q: Letf(x, y,z) be a function with the gradient vector . What are the extreme points of f with…

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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: 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: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

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Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

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Q: Evaluate the directional derivative Duf (2, 3) if ƒ (x, y) = and u is the unit vector in the same…

A: Given problem:- Evaluate the directional derivative Duf(2, 3) if f(x, y) = x/(x2 - y) and u is the…

Q: Determine the equation for the line with normal vector n = [3,-4] passing through the point P(-1,-2)

A: Given.

Q: Find the gradient of the function g(x,y) = xy at the point (5, -1). Then sketch the gradient…

A: Solution :-

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

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Q: What does the gradient vector of a function represent? Create your own real-life example that…

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