A light source is located over the center of a circular table of diameter d = 12 feet (see figure). Find the exact height h (in feet) of the light source such that the illumination I at the perimeter of the table is maximum when k sin(x) s² where s is the slant height, a is the angle at which the light strikes the table, and k is a constant. h = I = ft S i

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A: Topic = Derivative

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A: We can condense the logarithmic expression in the below steps.

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A: Let C  be the curve defined by R→t=2e2t-3, 1-e2t, 2e2t.If the arc on C from the point P-1, 0, 2 to…

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A: Please see the below picture for solution.

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A: Topic = Derivative

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A: We need to evaluate:

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A: Given data, Point A(2,8)

Q: integrating

A:

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A: I am attaching image so that you understand each and every step.

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A: 3) xy'+(1+x)y=e-x. 4)xdy+(x2-3y)dx=0.

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A: We can solve the exponential equation in the below steps.

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A: according to bartleby guideline we do only first part      x2dy+(2xy-x+1)dx=0    given equation is…

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A: ∫u(x)v(x)dx=u∫v(x)dx-∫ddxu(x)∫v(x)dxdx ∫cotxdx=ln|sinx| ∫csc2xdx=-cotx

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Q: and all functions that have a derivative functions have the form 0

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Q: 1. Find the area of the region enclosed by the curves y = x² and y = x by integrating with respect…

A: Please see the below picture for detailed solution.