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The general formula for a volume of rotation is pi times the integral of y^2. The first step is to square y. this can be done by squaring the first term, squaring the last term and finding twice the pr...
The rate at which the area is increasing, dA/dt, can be written with terms we know or can find out easily: dA/dt=dA/dr x dr/dt.Area of a disc, A = (pi)r^2dA/dr=2(pi)rRate of change of radius, dr/d...
Note here: u_n indicates u subscript n.
(a) u_1 = 48 and the ratio, r = 0.6
Using a calculator, u_2 = 48 x 0.6 = 28.8
u_3 = 28.8 x 0.6 = 17.28
(b...
8x3-12x2-2x+D...(1)
2x+1...(2)
Assume 2x+1=0 so x=-1/2
8x3-12x2-2x+D=-2... when divided by (2)
substi...
To answer this question we require the chain rule, which states that dy/dx=(dy/du)*(du/dx)
To use this formula in our question, we can let y=ln(sin(3x))=ln(u) where u=sin(3x)
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