Differentiation and Reccurence Q 1 - 5

Unit 1 Revision Questions

1. Prove that the four points A(-3,1), B(3,4), C(5,1) and D(-1,-2) form a parallelogram, and find the point of intersection of the diagonals E.

2. Two mobile phone companies A and B have between them 300,000 customers. Each month company A loses 20% of its customers to company B but gains 30% of company B's customers. If this continues each month, find in the long how many customers each company will have,.

3. Given the volume of a drinking can is fixed at 330ml, prove that the surface area is given by

and find the values of the radius of the can r, and the

height of the can h, which will minimise the total surface.

4. Sketch the graph of and note on the graph the maximum and minimum turning points for .

Find algebraically the solution for using the same domain.

5. Three successive terms (U₂,U₃, and U₄) in the linear sequence

are 10, -1 and

Find the values of a and b, and find the limit of this sequence if it exists.

Find the first value in this sequence U₁.