DEPARTMENT OF MATHEMATICS
MATHS 208 SC 1. (a) [3 marks] Let a n = Assignment 4 solutions Due: 14/10/08
2n 2 n +1 . Then a n +1 = . Therefore (n + 1)! n!
lim
a n +1 2 n! 2 2 n n! 2 n +1 2n 2 2n = lim = 0 < 1 , and = lim = lim n = lim n a n ( n + 1)! n ( n
DEPARTMENT OF MATHEMATICS MATHS 208 SC 2008 Assignment 4 Due: Tuesday 14th October
1. [6 marks: 3 marks each] Use the ratio test to determine if the following series are convergent or divergent. (a)
n!
n =1
2n
(b)
ln(n) . n n =1 3
2. [8 marks: 4 marks ea
Department of Mathematics MATHS 208 Assignment 3 Solutions
1. a) The equation x3 xy + 4y 2 + xyz z 3 = 11 denes a function z = f (x, y ) implicitly. Use implicit dierentiation to nd the value z of when (x, y, z ) = (1, 2, 2). x Solution: F = x3 xy + 4y 2
MATHS 208
Department of Mathematics Assignment 3
Due:30 September 2008
Please hand in your assignment to the appropriate box outside the Student Resource Centre by 4 pm on the due date. SHOW ALL WORKING FOR CREDIT.
1. [6 marks] (a) The equation x3 xy + 4y