For this series, find
(a) the common ratio,
(b) the first term,
(c) the sum to infinity,
(d) the smallest value of n for which the sum of the first n terms of the series exceeds 1000.
6 (a)(b) Geometric Series
3sin(x + 45°) = 2
(b) Find, for 0 ≤ x 2π, all the solutions of
2sin2x + 2 = 7cosx
giving your answers in radians.
You must show clearly how you obtained your answers.
The volume of the cuboid is 81 cubic centimetres.
(a) Show that the total length, L cm, of the twelve edges of the cuboid is given by
L = 12x + 162/x2
(b) Use calculus to find the minimum value of L.
(c) Justify, by further differentiation, that the value of L that you have found is a minimum.
The straight line with equation y = x+ 4 cuts the curve with equation y = −x2 + 2x - 24 at the points A and B, as shown in Figure 3.
(a) Use algebra to find the coordinates of the points A and B.
The finite region R is bounded by the straight line and the curve and is shown shaded in Figure 3.
(b) Use calculus to find the exact area of R.
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