for the function given:  a) Show that the function has any vector derivative in the direction of the unit vector u = u1i + u2j at the point (0, 0). b) Is the function continuous at the point (0, 0)?

Q: The three components of the derivative of the vector-valued function u are positive at t = t0.…

A: Given: The three components of the derivative of the vector-valued function u are positive at t =…

Q: Determine if the derivative of the vector-valued function exists at the specified point. (Your…

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Q: Show that the graph of the vector-valued function r(t) = is a circle, and find its radius and…

A: The equation of a circle is defined by the equation, (x-h)2+(y-k)2+(z-l)2=r2 , where, (h,k,l) is the…

Q: Let h(x, y) be a differentiable function and let (xo, yo) be a point in the domain of h. Also, let u…

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Q: Find the diectional derivative of the function f (xiy,z)= sin (xy+2) at the point of P(1, al2 x4) a…

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Q: 6.Consider a function f: R2 R, where f(xy) = cos(xy). Let u = be a unit vector. Use the definition…

A: Here we will use Definition of Directional derivative of f(x , y) in the direction of vector <u1…

Q: What is the derivative of a function ƒ(x, y) at a point P0 in the direction of a unit vector u? What…

A: For a function z=f(x,y): the partial derivative with respect to x gives the rate of change of f in…

Q: Suppose that f(z,y) is differentiable, and suppose that the directional derivative of f at the…

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Q: Let r(t) be a vector-valued function such that the magnitude of r(t) does not change over time. Use…

A: if r'(t) = 0 then we can say that r'(t) is perpendicular to the function r(t) for all times t.

Q: Suppose ƒ is differentiable at (9, 9), ∇ƒ(9, 9) = ⟨3, 1⟩, and w = (1, -1). Compute the directional…

A: Given that ∇ƒ(9, 9) = ⟨3, 1⟩. Note that w = (1, -1) is not a unit vector. Its unit vector along same…

Q: Find the directional derivative of f (x, y, z) = 2z²x + y° at the point (2, 1, 2) in the direction…

A: Here, f(x, y, z) is given we have to find directional derivative of f(x, y, z) at point (2, 1,2) in…

Q: 2. Consider the function f(x, y) = a) Find the directional derivative of f in the direction of the…

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Q: Consider the vector-valued function. (a) Show that is continuous at t = -1. (b) Evaluate (R. RY(2).…

A: Like a scalar function, features like continuity and differentiability are also demonstrated by…

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

A: Directional derivative of f(x,y) at any point P in the direction of vector v is, =(∇f)P.(unit vector…

Q: ) Find the directional derivative of the function f(x, y) = sin²(xy) at the point P (2,7) -2i+j √5…

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Q: 2. [-/16.66 Points] DETAILS Find the directional derivative of the function at the given point in…

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Q: Let f (x,y,z) = xye² + yze*. From point (1,0,1), which unit vector points in the direction in which…

A: Consider the given information. fx,y,z=xyez+yzex The point is 1,0,1. The direction in which f…