June 2005 - C4: Answers

Q 1   : 2 - 9/4 x - 81/64 x² - 729/512 x³
 
Q 2   : (2, -2) & (-2, 2)
 
Q 3   : ln 54
 
Q 4   : ⅓√3
 
Q 5(a): ¼(e²+1)
   (b): 0.89022, 396243
   (c): 2.168
 
Q 6(a): -2 cost sin³t
   (b): y = -½x + 2
   (c): y =    4    ,  x>-4
            √4 + x²  
 
Q 7(a): B=(2,2,-2)
   (b): 1/3
   (c): √18 = √18
   (d): D = (6, -2, 2)
 
Q 8(a): dV1/dt = 20    dV2/dt = -kV   dV/dt = 20 - kV
   (b): A = 20/k,  B = -20/k
   (c): 108.2