x = (√3) sin 2t, y = 4cos2t, 0 ≤ t ≤ π
(a) Show that dy/dx = k(√3) tan 2t, where k is a constant to be determined.
(b) Find an equation of the tangent to C at the point where t = π3
Give your answer in the form y = ax + b, where a and b are constants.
(c) Find a Cartesian equation of C.6 (a) Parametric differentiation
The finite region R, shown shaded in Figure 3, is bounded by the curve, the x-axis and the lines x = 1 and x = 4
(a) Use the trapezium rule, with 3 strips of equal width, to find an estimate for the area of R, giving your answer to 2 decimal places.
(b) Find ∫x1/2ln2x dx
(c) Hence find the exact area of R, giving your answer in the form aln2 + b where a and b are exact constants.7 (a) Trapezium Rule
8. Relative to a fixed origin O, the point A has position vector (10i + 2j + 3k) and the point B has position vector (8i + 3j + 4k).
The line l passes through the points A and B.
(a) Find the vector AB.
(b) Find a vector equation for the line l.
The point C has position vector (3i + 12j + 3k).
The point P lies on l. Given that the vector CP is perpendicular to l,
(c) find the position vector of the point P.
8 (a)(b) Vectors
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