Calculate the line integral of the vector-function F(x, y, z) = (y² +2²) i-yzj + xk along the path L: x=t, y=2 cost, z = 2 sint (OSIS). Present your answer in the exact form (don't use a

Q: Find a non-zero vector B' which is perpendicular to A'= 2i'-3j'.

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Q: Find the increase rate of the scalar V at point P from origin to the point P(2,6; 9,8 ; 9,5) where…

A: According to question given that The origin to the point P(2,6 ;9,8 ; 9,5) where V=3, 3xy+ 2, 6xyz

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs for…

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Q: 5. Find the directional derivative of f(x, y) = y² + (x²/y), at the point (2, 1) in the direction of…

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Q: f f(x, y, z) = xy: on of vectorî - %3D

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Q: Find an expression for a unit vector normal, no, to the surface x = (4 – cos (v)) cos (u), y = (4 –…

A: The complete solutions are given below

Q: 3. Find the directional derivative of f(x, y) = cos(3x+4y) at the point (7/6, π/6) along the…

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Q: Calculate the directional derivatives of functions Inx f (x,y) = x²+ y? in the direction of the…

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Q: Find the directional derivative of the function f(x, y) = ln(x³ + y³) at the point (3, − 2) in the…

A: Use the gradient of function for finding the directional derivative.

Q: Consider the vector-valued function r(t)= for t in the interval [0, π]. Find the magnitude of its…

A: Given:The given vector valued function is, Objective:The aim is to determine the magnitude of the…

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 3x sin(xy)…

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Q: nd the increase rate of the scalar V at point P from origin to the point P(12 , 1,11 here V=…

A: As gradient of a scalar function gives the magnitude and direction of rate of change.