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# Supplementary problems she refers to the textbook by

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the Department of Mathematics and the Faculty of Arts & Science. Supplementary Problems. “SHE” refers to the textbook by Salas, Hille, and Etgen (10th Edition) 1. SHE 1.6: 11, 13, 17, 21, 23, 27, 35, 55, 65, 69, 71, 75, 83. 2. SHE 1.7: 1, 7, 15, 19, 23, 27, 33, 39, 41, 45, 49, 55, 59. Required Problems. Hand in solutions to all the problems below. 1. (a) SHE 1.5: 52 (b) SHE 1.6: 76 (c) SHE 1.7: 32, 54. 2. Suppose g is a function defined for all x > 0 which satisfies the following properties for all a , b > 0: g ( 1 ) = 0 , g ( a b ) = g ( a ) - g ( b ) . Determine whether the function f ( x ) = g ( x + x 2 + 1 ) is even, odd, or neither, and justify your answer. 3. Show that for all θ ( 0 , π ) , the area of a triangle with side lengths a and b and with included angle θ is A = 1 2 ab sin θ . (Hint: You need to consider two cases.)

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4. Solve the following equations or inequalities in the interval [ 0 , 2 π ) . (i) cos x + 1 = sin x . (ii) 2sin3 x - 1 = 0. (iii) tan x - 3cot x = 0. (iv) 2sin 2 x - 5sin x + 3 < 0. 5. Prove the following identities. (i) ( cos x + cos y ) 2 +( sin x + sin y ) 2 = 2 + 2cos ( x + y ) . (ii) 1 sec x + tan x + 1 sec x - tan x = 2sec x . (iii) cot x + 1 cot x - 1 = 1 + tan x 1 - tan x . (iv) 1 - tan x tan y = cos ( x + y ) cos x cos y .
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• Spring '08
• Abraham
• Academic dishonesty, Department of Mathematics, Assignment Mark

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