(a) ln(x2 + 3x + 5)
(b) cos x /x2
The equation f (x) = 0 can be written as x =[arsin(1 - 0.5x)]1/2
(b) Use the iterative formula
xn+1 =[arsin(1 - 0.5xn)]1/2, x0 = 0.8
to find the values of x1 , x2 and x3 , giving your answers to 5 decimal places.
(c) Show that α = 0.80157 is correct to 5 decimal places.
The graph consists of two line segments that meet at the point R (4, – 3), as shown in Figure 1.
Sketch, on separate diagrams, the graphs of
(a) y = f(x + 4)
(b) = y = |f(-x)|
On each diagram, show the coordinates of the point corresponding to R.
(a) Find f-1(x)
(b) Find the domain of f−1
The function g is defined by
g: x |→ex2-2, x ∈ ℝ
(c) Find fg (x), giving your answer in its simplest form.
(d) Find the range of fg.
where k and p are positive constants.
When the leaf is picked from the tree, its mass is 7.5 grams and 4 days later its mass is 2.5 grams.
(a) Write down the value of p.
(b) Show that k = 1/4 ln3
(c) Find the value of t when dm/dt = -0.6ln3
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