2(3x + 2)/(9x2 - 4) - 2/(3x + 1)
as a single fraction in its simplest form.
(a) Show that the equation f(x) = 0 can be written as
The equation x3 + 3x2 + 4x -12 = 0 has a single root which is between 1 and 2
(b) Use the iteration formula
with x0 = 1 to find, to 2 decimal places, the value of x1, x2, and x3.
The root of f(x) = 0 is α.
(c) By choosing a suitable interval, prove that α = 1 272 . to 3 decimal places.
y = ex√3sin3x , −π/3 ≤ x ≤ π/3
(a) Find the x coordinate of the turning point P on C, for which x 0
Give your answer as a multiple of π.
(b) Find an equation of the normal to C at the point where x = 0
The curve passes through the points P(−1.5, 0) and Q(0, 5P) as shown.
On separate diagrams, sketch the curve with equation
(a) y =|f(x)|
(b) y = f(|x|)
(c) y = 2f(3x)
Indicate clearly on each sketch the coordinates of the points at which the curve crosses or meets the axes.
(b) Hence show that
4cosec22θ cosec2θ = sec2θ
(c) Hence or otherwise solve, for 0 < θ < π,
4cosec22θ cosec2θ = 4
giving your answers in terms of π.
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