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The first step to answering this question is to get the equation in a simpler form. Aim to have it solely in terms of sin(x) and cos(x) with no fractional parts.                                           ...

We must use the factor theorem since that is what the question asks. So we take p(x) and think about the factors of 8 we then evaluate it at x=1 to start, then move onto x=-1,2,-2 and so on. We see that i...

The general formula for integration by parts is given as
∫u(dv/dx)dx = uv - ∫v(du/dx)dx
given that the equation to be solved is ∫x²sin2xdx, the values for u, v, du/dx and dv/dx can ...

The first thing to do for part a) is work out the vertical component of the velocity. By drawing a triangle where 30m/s is the hypotenuse with angles of 30 degrees, 90 degrees, and 60 degrees, and by appl...

By the power rule, the derivative of x^(n) is nx(n^1) and by the chain rule, the derivative of g(h(x)) is g'(h(x))h'(x).
Let g(x)=x^(1/2) and h(x)=3x+2 so that f(x)=g(h(x)).

Then by the power...