f09fea - 92-131 Final Exam Answers Fall 2009 Brent Sec 203...

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92-131 Final Exam Answers Fall 2009 Brent Sec. 203 & 207 1) ) ( sec ) ( 2 x x e e x f = 2) 6 2 1 3 ) ( x x x s = 3) )) 3 ( sin 4 ) 3 cos( 3 ( 4 x x e y x = 4) 2 2 2 4 ) 1 ( 2 3 ) ( + + + = t t t t t g 5) 4 4 ln 9 ln 9 x x x x y = = 6) x x x f 2 ln ) ( = 7) h x h x h hx x h x h x h x f h x f x f h h h 1 1 3 3 lim ] 1 [ ] 1 ) [( lim ) ( ) ( lim ) ( 3 3 2 2 3 0 3 3 0 0 + + + + = + + + = + = 2 2 2 0 3 2 2 0 3 ) 3 3 ( lim 3 3 lim x h hx x h h x h hx h h = + + = + + = 8) 1 2 1 2 2 2 2 2 2 1 2 = y x y x ye x e y x x d y d , 3 2 + = x y 9) a) 3 16 ) ( t t t v = b) 4 = t c) 2 4 1 8 ) ( 4 2 + = t t t S 10) Let 2 / 2 ) ( x e x f = . a) f increases for 0 < x , and decreases for 0 > x . b) 1 ) 0 ( = f is a relative maximum value. c) f is concave down for 1 1 < < x , there. For 1 1 > <
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