t) The volume of the solid obtained by rotating the region enclosed by y = 12x - 4x², y=0 bout the y-axis can be computed using the method of cylindrical shells via an integral b = 1.² a A V = th limits of integration a = 0 and b = 1 ?

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A: Given the vectors u+v and u-v are orthogonal and  u+v=u+v To find u and v .

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A: Let's evaluate given partial derivative.

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A: Given: Consider the following situation, which involves two options. Determine which option is less…

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A: we have f(t) =4(t+1)2 =4(t2+2t+1)

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A: To minimise dimensions minimise surface area  So differentiate surface area and equate to zero

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A: We have to find the curve of intersection of the surfaces  z=x2+y2  and  x2+y2+z2=14.

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A: we have x3+ex =0to check number of roots we can draw graph of both and check number of intersection

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Q: Q6A)If y = cos ¹) prove Zyy + z = 0.

A: See this solution in below

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Q: Switch the order of integration of the following integrals, then evaluate: a) xsin(y) dydx = }}

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Q: Question 2 a) [ ] Show that the equation 4x - 8y + 12z + 2x² + 2y² + 2z² = -20 represents a sphere,…

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A: To find f(x) and value of a.