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Before starting to solve this problem, student should acknowledge that there are more than a variable, which satisfies the condition x^3. There are two ways to obtain this answer: (1) x^3 in the first mul...

To answer this question we must understand the representation of the unit circle firstly in real coordinates and secondly in the complex plane. The unit circle is just the drawing of a circle of radius 1 ...

a)   f'(x)=uv'+vu'     if    f(x)= uv

u=2x  u'=2  v=sin(x)   v'=cos(x)

g'(x)=2x cos(x) +2sin(x)

b)   g'(π) = 2π cos(π)+2sin(π)  = 2 π (-1) + 2 (0)

      g'(π) = -2π

in an inverse function, simply put the x and y are inversed: meaning x becomes y, and y becomes x

f(x): y=3x-5

f-1(x): x=3y-5 <=> x+5=3y <=> (x+5)/3 = y <=>

To integrate the volume of revolution first imagine a thin disk around the x-axis which we want to know the volume of: Volume=area x height. The area of a circle is given by pi r^2 and in our case let us ...