(a) Complete the table below, giving the values of y to 2 decimal places.
(b) Use the trapezium rule, with all the values of y from your table, to find an approximate value for
Figure 2 shows a sketch of part of the curve with equation y = 5/(3x2 - 2), x > 1
At the points A and B on the curve, x = 2 and x = 3 respectively.
The region S is bounded by the curve, the straight line through B and (2, 0), and the line through A parallel to the y-axis. The region S is shown shaded in Figure 2.
(c) Use your answer to part (b) to find an approximate value for the area of S.
can be written in the form 4 sin2 x + 7 sin x + 3 = 0
(b) Hence solve, for 0 ≤ x < 360°,
3 sin2 x + 7 sin x = cos2 x - 4
giving your answers to 1 decimal place where appropriate.
Given that AB is a diameter of the circle C,
(a) show that the centre of C has coordinates (3, 6),
(b) find an equation for C.
(c) Verify that the point (10, 7) lies on C.
(d) Find an equation of the tangent to C at the point (10, 7), giving your answer in the form y = mx + c, where m and c are constants.
V = 4x(5 - x)2
(a) Find dV/dx
(b) Hence find the maximum volume of the box.
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