5.) Find the volume of the solid in the first octant bounded by 2x + 3y + 4z = 12 and the coordinate planes by double integration.

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Q: Q4- Solve the following differential equation: (1+x²)dy + (y - tan-¹(x)) dx |dx = 0

A: To solve the following differential equation: 1+x2dy+y-tan-1xdx=0

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A: Above question is solved.

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Q: 7. Given a = (0, 1, 3), b = (4, 5, 6), then a · b = a. 1 b. 24 8. Given a = (0, 1, 3), b = (4, 5,…

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A: Given, f(x)=ln(x2+4x+14) on [-4,2]

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A: Given, Evaluate,

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Q: Q3- Sketch the region of integration and evaluate the integral: In8 lny [TD [t ex+y dxdy

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Q: 3. a. b. Evaluate the following integrals 2dx dx cos²x√4 tanx - tan² x sin(√x)dx J I sin

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Q: 22 Determine if lim(x,y)→(0,0) x²y² 2X4+Y4 exist

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