A scalar field is given by f = x2/3 + y2/3, where x and y are the Cartesian coordinates. The derivative of f along the line y = x directed away from the origin, at the point (8, 8) is

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: (플몰) V2 v2 2' 2 f(x, y) = x² – 3y², u и —

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Q: Find the directional derivative of the function z(x, y)=etan(y) + (x + 1)²sin(2y) at the point P(0,…

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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: State what it means for a scalar function y = f (x) to beintegrable on an interval [a, b].

A: Scalar integrable  function y = f (x)

Q: Find the directional derivative of the scalar field = xy + 4xz at the point (2, -2, 4) along the…

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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: (a) Find the directional derivative of z = x²y at (5,5) in the direction of π/2 with the positive…

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Q: tangent plane

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Q: Find the directional derivative of the function z(x, y) = e³tan(y) + (x + 1)²sin(2y) at the point…

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Q: Find the directional derivative of the function pez(x, y) = cos(2x) In (5y) + sin ¹(3x) (1-²)¹/2 at…

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Q: Find the domain of the vector function. lim t->infinity

A: Answer

Q: Find the directional derivative of o = x2 + 2xyz – yz? at the point (1, 1, 2) in the direction of…

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