طلب مساعدة !!
Question-1: A linear recurrence sequence is given by : (a) Obtain the parameters r and d and write down a recurrence relation for the sequence. [4marks] (b) Find the closed form for the sequence . [4marks] (c) Using (b): (i) compute the 5th and 10th terms . [2marks] (ii) deduce the long term behaviour of the sequence. [2marks] (d) Use Mathcad to list and plot the first 10 terms of the sequence. Compare with (c). [3marks] Question-2: The circle S has equation : . (a) Show that are ends of a diameter. [4marks] (b) Show that lies on S and determine angle ACB. [4marks] (c) Find the distance from to the nearest point E on S. [3marks] (d) Find the the x-coordinates of the points of intersection of S with the line joining D and F(0,2). [4marks] Question-3: (a) Show that the function : is 1-1 and find its inverse. [4marks] (b) Evaluate (i) (ii) [4marks] (c) Obtain parametric equations for the circle S with equation: [4marks] (d) Show that the center of the circle S lies on the line with parametric equations : . [3marks] Question-4: In this question and . (a) Describe a sequence of scalings and translations that would transform the graph of f(x) into the graph of g(x). [4 marks] (b) Obtain the domain and range of . [4marks] (c) Solve the equation: [4marks] (d) Use Mathcad to solve the equation : [3marks] |
ممكن حل هذي المسائل .. او مفاتيح الحل !!!
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