I = 16 –16(0.5)t , t ≥ 0
Use differentiation to find the value of dI/dt when t = 3.
Give your answer in the form ln a , where a is a constant.2. Differentiation
(b) Hence find ∫ 5/[(x + 1)(3x + 2)] dx, where x > 1.
(c) Find the particular solution of the differential equation
(x - 1)(3x + 2) dy/dx = 5y, x > 1
for which y = 8 at x = 2 . Give your answer in the form y = f(x).
4. Relative to a fixed origin O, the point A has position vector i - 3j + 2k and the point B has position vector -2i + 2j - k. The points A and B lie on a straight line l.
(a) Find AB.
(b) Find a vector equation of l.
The point C has position vector 2i + pj - 4k with respect to O, where p is a constant.
Given that AC is perpendicular to l, find
(c) the value of p,
(d) the distance AC.
in ascending powers of x, up to and including the term in x3. Give each coefficient as a simplified fraction.
f(x) = (a + bx)/(2 -3x)2, |x| < 2/3 , where a and b are constants.
In the binomial expansion of f ( ) x , in ascending powers of x, the coefficient of x is 0 and the coefficient of x2 is 9/16. Find
(b) the value of a and the value of b,
(c) the coefficient of x3 , giving your answer as a simplified fraction.
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