Download Automorphic Forms on GL(2) by H. Jacquet, R. P. Langlands PDF

By H. Jacquet, R. P. Langlands

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5 y y y x 2 x 2 2 2x 5 4 (ii) (iv) (vi) y y y 2x 3 x 1 3 x 2 Solve the following inequalities. (i) (iii) (v) 6 (ii) Sketch each of the following graphs on a separate set of axes. 1 a Ͻ b, where x 3 Ͻ x 4 2x 1 р 2x 3 2x Ͼ x 3 Solve the inequality x Ͼ 3x (ii) (iv) (vi) x 5 Ͼ x 2 2x р x 3 2x 5 у x 1 2 . [Cambridge International AS & A Level Mathematics 9709, Paper 2 Q1 June 2005] 7 Solve the inequality 2x Ͼ x 1 . [Cambridge International AS & A Level Mathematics 9709, Paper 3 Q2 June 2006] 8 Given that a is a positive constant, solve the inequality x 3a Ͼ x a .

Draw up a table and plot the values of log10z against log 10d. Use these points to suggest a value for D. It is known that, for d Ͻ D, n is a whole number. Use your graph to find the value of n. Show also that k 5 10 –9. 0. [MEI] 11 The variables x and y satisfy the relation 3y (i) (ii) 4x 2. By taking logarithms, show that the graph of y against x is a straight line. Find the exact value of the gradient of this line. Calculate the x co-ordinate of the point of intersection of this line with the line y = 2x, giving your answer correct to 2 decimal places.

The variables t and A satisfy the equation A = kb t, where b and k are constants. (i) Show that the graph of log A against t produces a straight line. 75). l g 2 (ii) 6 Find the values of b and k. All but one of the following pairs of readings satisfy, to 3 significant figures, a formula of the type y A x B. 28 Find the values of A and B, explaining your method. If the values of x are correct, state which value of y appears to be wrong and estimate what the value should be. [MEI] 37 An experimenter takes observations of a quantity y for various values of a variable x.

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