Given: F(x, y, z) = e²² + sin(4x + 6y − 2) - - x ln(2y - 3) 3 and P(-3,2,0). (a) Find the rate of change of F at P in the direction of the vector from P to Q(0, 4, −6). (b) Find the unit vector in the direction where F decreases most rapidly at P. (c) Find an equation of the plane tangent to the surface S: F(x, y, z) = 1 at P.

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Q: a) d) 125° 3/2 b) 34 +35 1 log₂ 32 G f) 24 log, √16

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Q: Given a 4x4 matrix as follows: Row 1 (4.2,20,-42.5,-16); Row 2 (-2,0,4.6,-32); Row 3…

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Q: (a) y'=ty (3-y), (b) y'=y (3-ty), (c) y'= -y (3-ty), (d) y'=t-1-y², y(0) = yo y(0) = yo y(0) = yo…

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Q: Describe and compare the solution sets of x₁ + 2x2 - 5x3 = 0 and X₁ + 2x₂ - 5x3 = -3. X₁ Describe…

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