(a) Find the gradient of the curve at P.
(b) Hence find the equation of the normal to C at P, giving your answer in the form ax + by + c = 0, where a, b and c are integers.
(b) Using your answer to part (a), find ∫x2 cos 3x dx
1/(2 - 5x)2, |x| < 2/5
in ascending powers of x, up to and including the term in x2, giving each term as a simplified fraction.
Given that the binomial expansion of (2 + kx)/(2 - 5x)2, |x| < 2/5 is
1/2 + 7/4x + Ax2 + ...
(b) find the value of the constant k,
(c) find the value of the constant A.3 (a) Binomial Expansion
Figure 1 shows the curve with equation
y = [2x/(3x2 + 4)], x ≥ 0
The finite region S, shown shaded in Figure 1, is bounded by the curve, the x-axis and the line x = 2
The region S is rotated 360° about the x-axis.
Use integration to find the exact value of the volume of the solid generated, giving your answer in the form k ln a, where k and a are constants.Volume of Revolution
Figure 2 shows a sketch of the curve C with parametric equations
x = 4 sin (t + π/6), y = cos 2t, 0 ≤ t < 2π
(a) Find an expression for dy/dx in terms of t.
(b) Find the coordinates of all the points on C where dy/dx = 05 (a) Parametric Curves
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