review1answerf10 - ; 1 ) domain, range of f 1 : [0 ; 1 ), [...

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Review 1 Answers, Fall 2010 1) a) 5 4 b) ¡ 1 c) ¡ 1 2 d) 12 e) ¡ 6 f) does not exist g) 0 h) 0 i) 1 2) a) 2 b) 1 2 c) + 1 d) ¡ 1 x = ¡ 1: removable, x = 0: removable, x = 1: inflnite vertical asymptote: x = 1, horizontal asymptote: y = ¡ 1 3) a) graph of f ( x ) = cos x is shifted right 2 units, and stretched vertically by a factor of 2 b) -4 y 3 -1 1 2 2 0 3 4 -2 1 -3 0 -4 -2 -1 x -3 4 c) graph of y = j x j is shifted right three units, re±ected over the x -axis, and then shifted up 2 units 4) x = 0 ; 4 ;…; 5 4 ; 2 5) x = 2 only 6) a) ( ¡1 ; ¡ 4) [ (8 ; 1 ) b) h 0 ; 4 · [ ± 2 ; 3 4 7) 1 p 5 8) a) [ ¡ 3 ; 0) [ [3 ; 1 ) b) (0 ;e 3 2 ) [ ( e 3 2 ; 1 ) 9) ( f g )( x ) = 1 + x 2 + x , domain: ( ¡ 2 ; 1 ) ( g f )( x ) = 1 p 3 ¡ x 2 , domain: ( ¡ p 3 ; p 3) 10) odd 11) a) does not exist b) ¡1 f ( x ) has a jump discontinuity at x = 0 and an inflnite discontinuity at x = 2.
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12) f ( x ): domain ( ¡1 ; 1 ), range ( ¡1 ; 2) f ¡ 1 ( x ) = ln(2 ¡ x ) ¡ 3, domain ( ¡1 ; 2), range ( ¡1 ; 1 ) graph of f , f ¡ 1 : 13) f ¡ 1 ( x ) = e x 2 ¡ 2 domain, range of f : [ e ¡ 2 ; 1 ), [0
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Unformatted text preview: ; 1 ) domain, range of f 1 : [0 ; 1 ), [ e 2 ; 1 ) 14) 3 2 15) a = 1 and b = 3 16) x = 0: jump, x = 1: removable; can dene f (1) = 3, cannot so redene f (0) f is continuous from the left at x = 0 f is continuous on ( 1 ; 0], (0 ; 1) and (1 ; 1 ) 17) A = 15(4) t 10 ; will take 10ln 5 ln4 11 : 6 days 18) a) 32 16 h ft/sec b) 32 ft/sec 19) y = 1 9 x + 2 9 20) a) y = 4 and y = 0 b) none c) y = 0 21) VA: x = 1 only HA: y = 3 and y = 1 22) b) [1 ; 3] and d) [ 3 ; 2] 23) A ( x ) = x 1500 3 2 x If area is 375,000 sq. ft., the dimensions are 500 ft by 750 ft. with x = 500....
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review1answerf10 - ; 1 ) domain, range of f 1 : [0 ; 1 ), [...

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