examen-de-maison1 - ECN1070: Solution de lexamen maison 1...

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Unformatted text preview: ECN1070: Solution de lexamen maison 1 Maxime Desmarais-Tremblay 21 octobre 2009 Note : Vous trouverez ici une br` eve solution des exercices et non une explica- tion des d emarches. Si vous ne comprenez pas ce qui sy trouve, nh esitez pas ` a en discuter entre vous ou ` a venir me poser des questions. Les r eponses qui suivent constituent une approche pour r esoudre les probl` emes. Dautres solutions sont egalement acceptables. Exercice 2 p. 112 (2 pts) f ( x ) = lim h f ( x + h )- f ( x ) h = lim h 1 / ( x + h )- 1 /x h = lim h x- ( x + h ) x ( x + h ) h = lim h - h x ( x + h ) 1 h =- 1 x 2 Exercice 6 p. 113 (4 pts) a) Soit f ( x ) = ax 2 + bx + c f ( x + h )- f ( x ) h = a ( x + h ) 2 + b ( x + h ) 2 + c- ( ax 2 + bx + c ) h = 2 axh + ah 2 + bh h = 2 ax + b + ah f ( x ) = lim h f ( x + h )- f ( x ) h = lim h (2 ax + b + ah ) = 2 ax + b 1 b) f ( x ) = 0 2 ax + b = 0 x =- b/ 2 a En ce point, la fonction atteindra soit un maximum, soit un minimum. Exercice 8 p. 126 (6 pts) a) lim x 2 x 2- 2 x x 3- 8 = lim x 2 x ( x- 2) ( x 2 + 2 x + 4)( x- 2) = lim x 2 x x 2 + 2 x + 4 = 1 6 b) lim h 3 27 + h- 3 h posons u = 3 27 + h u 3 = 27 + h h = u 3- 27 On a donc que u 3 lorsque h lim h 3 27 + h- 3 h = lim u 3 u- 3 u 3- 27 = lim u 3 u- 3 ( u- 3)( u 2 + 3 u + 9) = lim u 3 1 u 2 + 3 u + 9 = 1 27 c) lim x 1 x n- 1 x- 1 = lim x 1 ( x- 1)(1 + x + x 2 + + x n- 1 ) x- 1 = lim x 1 (1+ x + x 2 + + x n- 1 ) = n Exercice 8 p. 154 (3 pts) a) la fonction b ( t ) = B ( s ( t )) repr esente la consommation de carburant en fonction du temps....
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This note was uploaded on 02/12/2011 for the course ECN 1075 taught by Professor Barnabé during the Spring '10 term at Université de Montréal.

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examen-de-maison1 - ECN1070: Solution de lexamen maison 1...

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