Given that theta is small and is measured in radians, use the small angle approximations to find an approximate value of (1 - cos 4theta)/(2theta sin 3theta). (3)

In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. The curve C has equation y = f(x) where x is real. Given that f'(x) = 2x + (1/2)cos x, the curve has a stationary point with x coordinate alpha, and alpha is small, (a) use the small angle approximation for cos x to estimate the value of alpha to 3 decimal places. (3) The point P(0, 3) lies on C. (b) Find the equation of the tangent to the curve at P, giving your answer in the form y = mx + c, where m and c are constants to be found. (2)

Given that theta is small and in radians, use the small angle approximations to find an approximate numerical value of (theta tan 2theta)/(1 - cos 3theta). (3)