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# review1answerspring11 - f Â 1[0 1 e Â 2 1 15 Â 3 2 16 a = Â...

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Review 1 Answers, Spring 2011 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 = p x is shifted right three units, re±ected over the x -axis, and then shifted up 2 units 4) a) f ( x ) = ¡ x 2 + 2 x ¡ 2 (2 x ¡ 1) 5 3 b) No solution in the real number system 5) x = 3 ; 5 3 6) x = 2, x = ¡ 1 is extraneous 7) a) ( ¡1 ; ¡ 4) S (8 ; 1 ) b) [0 ; 4 ) S ( 2 ; 3 4 ) 8) 1 p 5 9) a) [ ¡ 3 ; 0) [ [3 ; 1 ) b) (0 ;e 3 2 ) [ ( e 3 2 ; 1 ) 10) ( f g )( x ) = 1 + x 2 + x , domain: ( ¡ 2 ; 1 ) ( g f )( x ) = 1 p 3 ¡ x 2 , domain: ( ¡ p 3 ; p 3)

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11) odd 12) a) does not exist b) ¡1 f ( x ) has a jump discontinuity at x = 0 and an inﬂnite discontinuity at x = 2. 13) 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 : 14) f ¡ 1 ( x ) = e x 2 ¡ 2 domain, range of f : [ e ¡ 2 ; 1 ), [0 ; 1 ) domain, range of
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Unformatted text preview: f Â¡ 1 : [0 ; 1 ), [ e Â¡ 2 ; 1 ) 15) Â¡ 3 2 16) a = Â¡ 1 and b = Â¡ 3 17) x = 0: jump, x = 1: removable; can deï¬‚ne f (1) = 3, cannot so redeï¬‚ne f (0) f is continuous from the left at x = 0 f is continuous on ( Â¡1 ; 0], (0 ; 1) and (1 ; 1 ) 18) A = 15(4) t 10 ; will take 10ln 5 ln4 â€¦ 11 : 6 days 19) b) [1 ; 3] and d) [ Â¡ 3 ; Â¡ 2] 20) A ( x ) = x Â± 1500 Â¡ 3 2 x Â¶ If area is 375,000 sq. ft., the dimensions are 500 ft by 750 ft. with x = 500. 21) x 2 ( Â¡ â€¦ 8 Â¡ 1 2 ) + 10 x ft 2 22) a) 16 ft/sec b) Â¡ 32 Â¡ 16 h ft/sec c)-32 ft/sec 23) a) Day 0: no items, day 1: â€¦ 5 : 53 items b) Â¡ 4ln( 3 5 ) â€¦ 2 : 04 days c) 25 items d) 24) a) y = 4 and y = 0 b) none c) y = 0...
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review1answerspring11 - f Â 1[0 1 e Â 2 1 15 Â 3 2 16 a = Â...

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