Find Duf at (2,−1,1) for f(x, y, z) = 3x5y²z³ in the direction given by u = (1/3, 2/3, −2/3).

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A: We know directional derivative formula Du→fa, b, c=∇fa, b, c.u^ Lets say u→=cosθ, sinθ be the…

Q: f(r, y) : = V3x? + 4y? fz(3, – 2) =|

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Q: Find dy 3 2. -3x

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Q: Evaluate (2x - y) dx + (x + 7y) dy. C C: x-axis from x = 0 to x = 2

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A: On the curve Gamma , which is straight line from (0, 0) to (3,0) we have, y=0 and x  ranges from 0…

Q: Consider (x, y, z) = 4xy²+ 3y sin(z) and at the point P = (1,2,0) calculate the directions in which…

A: Approach to solving the question:To find the directions in which the…

Q: let r (t) = The y component of r' (5)

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Q: The temperature at the point (x, y) on a metal plate is given by T (x, y) = y/(x2 + y2 ). Find the…

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Q: 5. Find the linear approximation of f (x, y, z) = x³y² + 22 at the point (2, 3,4). Use this to…

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