BUSI3119-E1 ADVANCED CALCULUS FOR BUSINESS, ECONOMICS AND FINANCE 2019-2020
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BUSI3119-E1
A LEVEL 3 MODULE, AUTUMN SEMESTER 2019-2020
ADVANCED CALCULUS FOR BUSINESS, ECONOMICS AND FINANCE
1. (a) Use L’Hopital rule to find the lix( − )
(8 Marks)
(b) Show that det(adj(A)) = (det(A))n- 1.
(12 Marks)
2. (a) Compute the rank of the following matrix: (6 Marks) | 1 1 |
(b) Find the solution of the following system: (6 Marks)
w − x + 3y− z = 0
w + 4x− y + 2z= 3
3w + 7x+ y + z = 6.
(c) Given that A = [], compute A100. (8 Marks)
3. Find the general solution of each of the following differential equations, then, find the solution that satisfies y(1) = 1:
(a) y.= t− y (8 Marks)
(b) ty.+ (1 − t)y = e2t (12 Marks)
4. Find the general solution of y…− y.− 2y = 6t+ 4e- t . (20 Marks)
5. Solve the following control problem using the current value formulation (20 Marks)
max j0T (2u − u2 + 2x)e- 2tdt, x.= x − u, x(0) = 0, x(T) free, u ∈ ( −∞, ∞)
2022-08-02