(c) The electric potential V at the point P(x, y, z) in a rectangular coordinate system is given by V = x2 + 4y² + 9z. Calculate the rate of change of V at P(2,–1,3) in the direction from P to the origin.

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A: Given: The given function is fx,y=x+sin(x+2y) at P(0,0).

Q: f(x, y) = 3eª cos y, (a, b) = (0,7), and v = (3, 3). a. Calculate the directional derivative of f at…

A:

Q: f(x, y) = 5eª cos y, (a,b) = (0, 7), a. Calculate the directional derivative of f at the point (a,…

A:

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

A: The maximum value of a function f occurs in the direction of the gradient of the function f and this…

Q: Find r'(t)'r" (t) given the following vector function. r(t) = 3cos(t)i+ 4sin(t)j cost sint -25cost…

A: Given vector function is, r(t)=3cost i+4sint j

Q: (c) Differentiate y = Vsec3 (5t2)

A:

Q: Let r(t) = (-3t5 - 1, 2e³, 4 sin(4t)) Find the unit tangent vector T(t) at the point t = 0 T(0) -

A: If  is vector valued function which is differentiable and then the unit tangent of is given by

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 linear approximation of the function at the given point: f(x, y) = 2 sin x – 3 cos y at (0,…

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