Homework_Set_1 - Z π fl fl 1 2 cos t fl fl dt(b Z dx x...

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Math 1a Fall 2005 HOMEWORK SET 1 DUE AT NOON ON MONDAY, OCTOBER 3, 2005 (1) Prove that 3 - 6 is irrational. This should be a carefully written out argument. You can use things proven in class. Hint: Look at its square. (2) Apostol page 36, problem 6. (3) Compute the following integrals: (a)
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Unformatted text preview: Z π fl fl 1 2 + cos( t ) fl fl dt (b) Z dx x log x (c) Z e √ x dx (4) Compute the derivatives of the following functions: (a) e e x (b) e log x (c) r x + q x + √ x (d) sin(sin(sin( x )))) (5) Use mathematical induction to prove that d dx x n = nx n-1 1...
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