Let w = (x + 2y + 3z) dx A dy + (cos(x) + sin(y) + e²)dy ^ dz. (a) Write dw as f(x, y, z) dx A dy A dz in rectangular coordinates. (b) Write dw as h(p, 6,0) dp ^ do A do in spherical coordinates.

Q: 3. 5y“ y = 5y^2 4. 4x*y°m', 8xy°m', x’y´m 4 3 7 т, 5 3 т, 5.2, а, ь, с b’, c

A: LCM :  least common multiple of two or many number is known as LCM .    3.    LCM of  5 y2 , y = 5y2…

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A: The given polar equation is: r=21-cosθ

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A: Answer:We have to convert∫50∫25-y20∫50-x2-y2x2+y2x2+y2+z2 dzdxdy into sphercal coordinates∵0≤y≤5…

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Q: dy (ii) Find dx? for the parametric equations x = t+ sin t, y= 1+cost

A: • This problem can be solved by using Chain rule as explained in step 2.

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A: The position vector for particle moving on helix is ct=3cost, 2sint, t2. To find the speed of the…

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Q: (ii) Find for the parametric equations dx2 dy x =t – sint, y = 1 – cost

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