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We know that having cos and sin functions in a question is going to cause us problems - we need a single function of x. So, step 1, we need to rewrite sin or cos in terms of the other. How do we choose wh...
We know from trigonmetric identities that cos(2x) = 2cos^2(x) -1, therefore cos^2(x) = 0.5(1+cos(2x)).
Subbing this in gives the following integrand: 0.5(1+cos(2x))sin(2x).
We can now split ...
By the chain rule ds/dt = ds/dr * dr/dv * dv/t. At a height of r, the water fills a hemisphere. So ds/dr = 6pir. dr/dv = 1/(dv/dr), so we need to find dv/dr. Students should have the formula for the v...
The first step to solving this is equation is to notice that the equation is of a similar to the form of a quadratic equation: ay^2 + by + c = 0 where a, b and c are constants. Next we introduce a new va...
Let u = x2+4x+2 so y = ln(u).
Then dy/du = 1/u and du/dx = 2x+4.
Using the chain rule we have:
dy/dx = (dy/du)*(du/dx)
= (1/u)*(2x+4)
= (2x+4)/(x2+...
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