The point P lies on C and has coordinates (w, – 32).
(a) the value of w,
(b) the equation of the tangent to C at the point P in the form y mx c = + , where m and c are constants.
2. g(x) = ex-1 + x - 6
(a) Show that the equation g(x) = 0 can be written as
x = ln(6 -x) + 1, x < 6
The root of g(x) = 0 is α.
The iterative formula
xn + 1 = ln(6 -xn) + 1, x0 = 2
is used to find an approximate value for α.
(b) Calculate the values of x1 , x2 and x3 to 4 decimal places.
(c) By choosing a suitable interval, show that α = 2.307 correct to 3 decimal places.
The curve passes through the points Q(0, 2) and P(−3, 0) as shown.
(a) Find the value of ff(−3) .
On separate diagrams, sketch the curve with equation
(b) y = f-1(x)
(c) y = f(|x|) - 2
(d) y = 2 f(½ x)
Indicate clearly on each sketch the coordinates of the points at which the curve crosses or meets the axes.
Give the value of α to 3 decimal places.
(b) p(θ) = 4/(12 + 6cosθ + 8 sinθ, 0 ≤ θ ≤ 2π
(i) the maximum value of p(θ),
(ii) the value of θ at which the maximum occurs.
5. (i) Differentiate with respect to x
(a) y = x3ln2x
(b) y = (x + sin2x)3
Given that x = cot y ,
(ii) show that dy/dx = -1/(1 + x2)
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