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| Unknown | 1996-08-19 | 15.5 KB |
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| Confidence | Program | Detection | Match Type | Support
|
|---|
| 1%
| dexvert
| Eclipse Tutorial (other/eclipseTutorial)
| ext
| Unsupported |
| 1%
| dexvert
| JuggleKrazy Tutorial (other/juggleKrazyTutorial)
| ext
| Unsupported |
| 100%
| file
| data
| default
| |
| 100%
| gt2
| Kopftext: 'TUTOR 06'
| default (weak)
|
|
hex view+--------+-------------------------+-------------------------+--------+--------+
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|00000020| 63 72 69 74 69 63 61 6c | 20 6e 75 6d 62 65 72 73 |critical| numbers|
|00000030| 20 28 72 6f 75 6e 64 65 | 64 20 74 6f 20 74 77 6f | (rounde|d to two|
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|00000cf0| 72 20 65 71 75 61 6c 20 | 74 6f 20 7a 65 72 6f 20 |r equal |to zero |
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|00000da0| 20 32 11 33 78 20 11 31 | 2b 20 31 20 69 73 20 67 | 2.3x .1|+ 1 is g|
|00000db0| 72 65 61 74 65 72 20 74 | 68 61 6e 20 6f 72 20 65 |reater t|han or e|
|00000dc0| 71 75 61 6c 20 74 6f 20 | 7a 65 72 6f 20 66 6f 72 |qual to |zero for|
|00000dd0| 20 61 6c 6c 0d 0a 00 72 | 65 61 6c 20 6e 75 6d 62 | all...r|eal numb|
|00000de0| 65 72 73 2e 20 20 54 68 | 65 20 73 6f 6c 75 74 69 |ers. Th|e soluti|
|00000df0| 6f 6e 20 73 65 74 20 69 | 73 20 28 2d 11 34 38 11 |on set i|s (-.48.|
|00000e00| 31 2c 20 11 34 38 11 31 | 29 2c 20 77 68 69 63 68 |1, .48.1|), which|
|00000e10| 20 69 73 20 74 68 65 20 | 72 65 61 6c 20 6e 75 6d | is the |real num|
|00000e20| 62 65 72 20 6c 69 6e 65 | 2e 0d 0a 00 00 17 4f 06 |ber line|......O.|
|00000e30| 0d 0b 00 49 6e 63 6f 72 | 72 65 63 74 2e 20 20 49 |...Incor|rect. I|
|00000e40| 6e 20 66 61 63 74 6f 72 | 65 64 20 66 6f 72 6d 20 |n factor|ed form |
|00000e50| 77 65 20 68 61 76 65 20 | 11 33 78 11 31 28 11 33 |we have |.3x.1(.3|
|00000e60| 78 20 11 31 2b 20 33 29 | 20 3e 20 30 2c 20 77 68 |x .1+ 3)| > 0, wh|
|00000e70| 69 63 68 20 69 6d 70 6c | 69 65 73 20 74 68 61 74 |ich impl|ies that|
|00000e80| 20 74 68 65 0d 0a 00 63 | 72 69 74 69 63 61 6c 20 | the...c|ritical |
|00000e90| 6e 75 6d 62 65 72 73 20 | 61 72 65 20 11 33 78 20 |numbers |are .3x |
|00000ea0| 11 31 3d 20 30 20 61 6e | 64 20 11 33 78 20 11 31 |.1= 0 an|d .3x .1|
|00000eb0| 3d 20 2d 33 2e 20 20 54 | 68 75 73 2c 20 74 68 65 |= -3. T|hus, the|
|00000ec0| 20 74 65 73 74 20 69 6e | 74 65 72 76 61 6c 73 20 | test in|tervals |
|00000ed0| 61 72 65 20 0d 0a 00 28 | 2d 11 34 38 11 31 2c 20 |are ...(|-.48.1, |
|00000ee0| 2d 33 29 2c 20 28 2d 33 | 2c 20 30 29 2c 20 61 6e |-3), (-3|, 0), an|
|00000ef0| 64 20 28 30 2c 20 11 34 | 38 11 31 29 2e 20 20 54 |d (0, .4|8.1). T|
|00000f00| 65 73 74 69 6e 67 20 65 | 61 63 68 20 69 6e 74 65 |esting e|ach inte|
|00000f10| 72 76 61 6c 2c 20 77 65 | 20 66 69 6e 64 20 74 68 |rval, we| find th|
|00000f20| 61 74 20 74 68 65 20 0d | 0a 00 73 6f 6c 75 74 69 |at the .|..soluti|
|00000f30| 6f 6e 20 73 65 74 20 69 | 73 20 74 68 65 20 69 6e |on set i|s the in|
|00000f40| 74 65 72 76 61 6c 20 28 | 2d 33 2c 20 30 29 2e 0d |terval (|-3, 0)..|
|00000f50| 0a 00 00 17 4f 03 0d 0b | 00 52 69 67 68 74 2e 20 |....O...|.Right. |
|00000f60| 20 4e 6f 74 65 20 74 68 | 61 74 20 74 68 65 20 65 | Note th|at the e|
|00000f70| 6e 64 70 6f 69 6e 74 73 | 20 61 72 65 20 6e 6f 74 |ndpoints| are not|
|00000f80| 20 69 6e 63 6c 75 64 65 | 64 20 69 6e 20 74 68 65 | include|d in the|
|00000f90| 20 73 6f 6c 75 74 69 6f | 6e 20 73 65 74 2e 0d 0a | solutio|n set...|
|00000fa0| 00 00 17 4f 06 0d 0b 00 | 49 6e 63 6f 72 72 65 63 |...O....|Incorrec|
|00000fb0| 74 2e 20 20 49 6e 20 66 | 61 63 74 6f 72 65 64 20 |t. In f|actored |
|00000fc0| 66 6f 72 6d 20 77 65 20 | 68 61 76 65 20 11 33 78 |form we |have .3x|
|00000fd0| 11 31 28 11 33 78 20 11 | 31 2b 20 33 29 20 3e 20 |.1(.3x .|1+ 3) > |
|00000fe0| 30 2c 20 77 68 69 63 68 | 20 69 6d 70 6c 69 65 73 |0, which| implies|
|00000ff0| 20 74 68 61 74 20 74 68 | 65 0d 0a 00 63 72 69 74 | that th|e...crit|
|00001000| 69 63 61 6c 20 6e 75 6d | 62 65 72 73 20 61 72 65 |ical num|bers are|
|00001010| 20 11 33 78 20 11 31 3d | 20 30 20 61 6e 64 20 11 | .3x .1=| 0 and .|
|00001020| 33 78 20 11 31 3d 20 2d | 33 2e 20 20 54 68 75 73 |3x .1= -|3. Thus|
|00001030| 2c 20 74 68 65 20 74 65 | 73 74 20 69 6e 74 65 72 |, the te|st inter|
|00001040| 76 61 6c 73 20 61 72 65 | 20 0d 0a 00 28 2d 11 34 |vals are| ...(-.4|
|00001050| 38 11 31 2c 20 2d 33 29 | 2c 20 28 2d 33 2c 20 30 |8.1, -3)|, (-3, 0|
|00001060| 29 2c 20 61 6e 64 20 28 | 30 2c 20 11 34 38 11 31 |), and (|0, .48.1|
|00001070| 29 2e 20 20 54 65 73 74 | 69 6e 67 20 65 61 63 68 |). Test|ing each|
|00001080| 20 69 6e 74 65 72 76 61 | 6c 2c 20 77 65 20 66 69 | interva|l, we fi|
|00001090| 6e 64 20 74 68 61 74 20 | 74 68 65 20 0d 0a 00 73 |nd that |the ...s|
|000010a0| 6f 6c 75 74 69 6f 6e 20 | 73 65 74 20 69 73 20 74 |olution |set is t|
|000010b0| 68 65 20 69 6e 74 65 72 | 76 61 6c 20 28 2d 33 2c |he inter|val (-3,|
|000010c0| 20 30 29 2e 0d 0a 00 00 | 17 4f 03 0d 0b 00 53 6f | 0).....|.O....So|
|000010d0| 72 72 79 2c 20 6f 6e 65 | 20 6f 66 20 74 68 65 73 |rry, one| of thes|
|000010e0| 65 20 61 6e 73 77 65 72 | 73 20 69 73 20 63 6f 72 |e answer|s is cor|
|000010f0| 72 65 63 74 2e 20 20 54 | 72 79 20 61 67 61 69 6e |rect. T|ry again|
|00001100| 2e 0d 0a 00 00 17 4f 04 | 0d 0b 00 49 6e 63 6f 72 |......O.|...Incor|
|00001110| 72 65 63 74 2e 20 20 54 | 68 69 73 20 69 73 20 70 |rect. T|his is p|
|00001120| 61 72 74 20 6f 66 20 74 | 68 65 20 73 6f 6c 75 74 |art of t|he solut|
|00001130| 69 6f 6e 2c 20 62 75 74 | 20 74 68 65 20 73 6f 6c |ion, but| the sol|
|00001140| 75 74 69 6f 6e 20 73 68 | 6f 75 6c 64 20 61 6c 73 |ution sh|ould als|
|00001150| 6f 0d 0a 00 69 6e 63 6c | 75 64 65 20 28 30 2c 20 |o...incl|ude (0, |
|00001160| 32 29 2e 0d 0a 00 00 17 | 4f 03 0d 0b 00 47 6f 6f |2)......|O....Goo|
|00001170| 64 2e 20 20 54 68 69 73 | 20 69 73 20 74 68 65 20 |d. This| is the |
|00001180| 73 6f 6c 75 74 69 6f 6e | 20 73 65 74 20 66 6f 72 |solution| set for|
|00001190| 20 74 68 65 20 67 69 76 | 65 6e 20 69 6e 65 71 75 | the giv|en inequ|
|000011a0| 61 6c 69 74 79 2e 0d 0a | 00 00 17 4f 04 0d 0b 00 |ality...|...O....|
|000011b0| 49 6e 63 6f 72 72 65 63 | 74 2e 20 20 54 68 69 73 |Incorrec|t. This|
|000011c0| 20 69 73 20 70 61 72 74 | 20 6f 66 20 74 68 65 20 | is part| of the |
|000011d0| 73 6f 6c 75 74 69 6f 6e | 2c 20 62 75 74 20 74 68 |solution|, but th|
|000011e0| 65 20 73 6f 6c 75 74 69 | 6f 6e 20 73 68 6f 75 6c |e soluti|on shoul|
|000011f0| 64 20 61 6c 73 6f 20 0d | 0a 00 69 6e 63 6c 75 64 |d also .|..includ|
|00001200| 65 20 28 2d 11 34 38 11 | 31 2c 20 2d 32 29 2e 0d |e (-.48.|1, -2)..|
|00001210| 0a 00 00 17 4f 03 0d 0b | 00 53 6f 72 72 79 2c 20 |....O...|.Sorry, |
|00001220| 6f 6e 65 20 6f 66 20 74 | 68 65 73 65 20 61 6e 73 |one of t|hese ans|
|00001230| 77 65 72 73 20 69 73 20 | 63 6f 72 72 65 63 74 2e |wers is |correct.|
|00001240| 20 20 54 72 79 20 61 67 | 61 69 6e 2e 0d 0a 00 00 | Try ag|ain.....|
|00001250| 17 4f 04 0d 0b 00 57 72 | 6f 6e 67 2e 20 20 54 68 |.O....Wr|ong. Th|
|00001260| 65 20 63 72 69 74 69 63 | 61 6c 20 6e 75 6d 62 65 |e critic|al numbe|
|00001270| 72 73 20 61 72 65 20 11 | 33 78 20 11 31 3d 20 33 |rs are .|3x .1= 3|
|00001280| 20 61 6e 64 20 11 33 78 | 20 11 31 3d 20 36 2c 20 | and .3x| .1= 6, |
|00001290| 62 75 74 20 62 79 20 74 | 65 73 74 69 6e 67 20 74 |but by t|esting t|
|000012a0| 68 65 20 0d 0a 00 69 6e | 74 65 72 76 61 6c 73 20 |he ...in|tervals |
|000012b0| 28 2d 11 34 38 11 31 2c | 20 33 29 2c 20 28 33 2c |(-.48.1,| 3), (3,|
|000012c0| 20 36 29 2c 20 61 6e 64 | 20 28 36 2c 20 11 34 38 | 6), and| (6, .48|
|000012d0| 11 31 29 2c 20 77 65 20 | 67 65 74 20 74 68 65 20 |.1), we |get the |
|000012e0| 73 6f 6c 75 74 69 6f 6e | 20 28 33 2c 20 36 29 2e |solution| (3, 6).|
|000012f0| 0d 0a 00 00 17 4f 04 0d | 0b 00 57 72 6f 6e 67 2e |.....O..|..Wrong.|
|00001300| 20 20 54 68 65 20 63 72 | 69 74 69 63 61 6c 20 6e | The cr|itical n|
|00001310| 75 6d 62 65 72 73 20 61 | 72 65 20 11 33 78 20 11 |umbers a|re .3x .|
|00001320| 31 3d 20 33 20 61 6e 64 | 20 11 33 78 20 11 31 3d |1= 3 and| .3x .1=|
|00001330| 20 36 2c 20 62 75 74 20 | 62 79 20 74 65 73 74 69 | 6, but |by testi|
|00001340| 6e 67 20 74 68 65 20 0d | 0a 00 69 6e 74 65 72 76 |ng the .|..interv|
|00001350| 61 6c 73 20 28 2d 11 34 | 38 11 31 2c 20 33 29 2c |als (-.4|8.1, 3),|
|00001360| 20 28 33 2c 20 36 29 2c | 20 61 6e 64 20 28 36 2c | (3, 6),| and (6,|
|00001370| 20 11 34 38 11 31 29 2c | 20 77 65 20 67 65 74 20 | .48.1),| we get |
|00001380| 74 68 65 20 73 6f 6c 75 | 74 69 6f 6e 20 28 33 2c |the solu|tion (3,|
|00001390| 20 36 29 2e 0d 0a 00 00 | 17 4f 04 0d 0b 00 56 65 | 6).....|.O....Ve|
|000013a0| 72 79 20 67 6f 6f 64 2e | 20 20 54 68 65 20 73 6f |ry good.| The so|
|000013b0| 6c 75 74 69 6f 6e 20 73 | 65 74 20 69 73 20 61 6c |lution s|et is al|
|000013c0| 6c 20 72 65 61 6c 20 6e | 75 6d 62 65 72 73 20 67 |l real n|umbers g|
|000013d0| 72 65 61 74 65 72 20 74 | 68 61 6e 20 74 68 72 65 |reater t|han thre|
|000013e0| 65 20 61 6e 64 20 0d 0a | 00 6c 65 73 73 20 74 68 |e and ..|.less th|
|000013f0| 61 6e 20 73 69 78 2e 0d | 0a 00 00 17 4f 03 0d 0b |an six..|....O...|
|00001400| 00 4e 6f 2e 20 20 54 68 | 65 20 67 69 76 65 6e 20 |.No. Th|e given |
|00001410| 69 6e 65 71 75 61 6c 69 | 74 79 20 68 61 73 20 61 |inequali|ty has a|
|00001420| 20 73 6f 6c 75 74 69 6f | 6e 2e 20 20 54 72 79 20 | solutio|n. Try |
|00001430| 61 67 61 69 6e 2e 0d 0a | 00 00 17 4f 04 20 20 20 |again...|...O. |
|00001440| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001450| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001460| 20 20 20 20 20 20 20 11 | 34 28 20 20 20 20 29 0d | .|4( ).|
|00001470| 0b 00 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.. | |
|00001480| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001490| 20 20 20 20 20 20 20 20 | 20 20 20 20 21 11 31 35 | | !.15|
|000014a0| 20 20 20 11 34 21 0d 0b | 00 11 31 56 65 72 79 20 | .4!..|..1Very |
|000014b0| 67 6f 6f 64 2e 20 20 54 | 68 65 20 73 6f 6c 75 74 |good. T|he solut|
|000014c0| 69 6f 6e 20 73 65 74 20 | 69 73 20 5b 2d 31 2c 20 |ion set |is [-1, |
|000014d0| 31 29 20 11 34 75 20 21 | 32 11 31 2c 20 11 34 38 |1) .4u !|2.1, .48|
|000014e0| 21 20 11 31 2e 0d 0b 00 | 20 20 20 20 20 20 20 20 |! .1....| |
|000014f0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001500| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001510| 20 20 11 34 21 11 31 32 | 20 20 20 11 34 21 0d 0b | .4!.12| .4!..|
|00001520| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |. | |
|00001530| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001540| 20 20 20 20 20 20 20 20 | 20 20 20 39 20 20 20 20 | | 9 |
|00001550| 30 0d 0a 00 00 17 4f 08 | 0d 0b 00 20 20 20 20 20 |0.....O.|... |
|00001560| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001570| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001580| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001590| 20 20 20 20 20 20 20 35 | 0d 0b 00 49 6e 63 6f 72 | 5|...Incor|
|000015a0| 72 65 63 74 2e 20 20 54 | 68 65 20 63 72 69 74 69 |rect. T|he criti|
|000015b0| 63 61 6c 20 6e 75 6d 62 | 65 72 73 20 61 72 65 20 |cal numb|ers are |
|000015c0| 11 33 78 20 11 31 3d 20 | 2d 31 2c 20 11 33 78 20 |.3x .1= |-1, .3x |
|000015d0| 11 31 3d 20 31 2c 20 61 | 6e 64 20 11 33 78 20 11 |.1= 1, a|nd .3x .|
|000015e0| 31 3d 20 11 34 32 11 31 | 2e 20 20 54 65 73 74 69 |1= .42.1|. Testi|
|000015f0| 6e 67 0d 0b 00 20 20 20 | 20 20 20 20 20 20 20 20 |ng... | |
|00001600| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001610| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001620| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001630| 20 32 0d 0b 00 20 20 20 | 20 20 20 20 20 20 20 20 | 2... | |
|00001640| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001650| 20 20 20 20 20 20 11 34 | 28 20 20 20 20 29 20 20 | .4|( ) |
|00001660| 20 20 20 20 28 20 20 20 | 20 29 0d 0b 00 20 20 20 | ( | )... |
|00001670| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001680| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 21 20 | | ! |
|00001690| 20 20 11 31 35 11 34 21 | 20 20 20 20 20 20 21 11 | .15.4!| !.|
|000016a0| 31 35 20 20 20 11 34 21 | 0d 0b 00 11 31 74 68 65 |15 .4!|....1the|
|000016b0| 20 69 6e 74 65 72 76 61 | 6c 73 20 28 2d 11 34 38 | interva|ls (-.48|
|000016c0| 11 31 2c 20 2d 31 29 2c | 20 28 2d 31 2c 20 31 29 |.1, -1),| (-1, 1)|
|000016d0| 2c 20 11 34 21 11 31 31 | 2c 20 11 34 32 21 11 31 |, .4!.11|, .42!.1|
|000016e0| 2c 20 61 6e 64 20 11 34 | 21 32 11 31 2c 20 11 34 |, and .4|!2.1, .4|
|000016f0| 38 21 11 31 2c 20 77 65 | 20 67 65 74 20 0d 0b 00 |8!.1, we| get ...|
|00001700| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001710| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001720| 20 11 34 21 20 20 20 11 | 31 32 11 34 21 20 20 20 | .4! .|12.4! |
|00001730| 20 20 20 21 11 31 32 20 | 20 20 11 34 21 0d 0b 00 | !.12 | .4!...|
|00001740| 20 20 20 20 20 20 20 20 | 20 20 28 20 20 20 20 29 | | ( )|
|00001750| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001760| 20 39 20 20 20 20 30 20 | 20 20 20 20 20 39 20 20 | 9 0 | 9 |
|00001770| 20 20 30 0d 0b 00 20 20 | 20 20 20 20 20 20 20 20 | 0... | |
|00001780| 21 11 31 35 20 20 20 11 | 34 21 0d 0b 00 11 31 5b |!.15 .|4!....1[|
|00001790| 2d 31 2c 20 31 29 20 11 | 34 75 20 21 32 11 31 2c |-1, 1) .|4u !2.1,|
|000017a0| 20 11 34 38 21 20 11 31 | 2e 0d 0b 00 20 20 20 20 | .48! .1|.... |
|000017b0| 20 20 20 20 20 20 11 34 | 21 11 31 32 20 20 20 11 | .4|!.12 .|
|000017c0| 34 21 0d 0b 00 20 20 20 | 20 20 20 20 20 20 20 39 |4!... | 9|
|000017d0| 20 20 20 20 30 0d 0a 00 | 00 17 4f 08 0d 0b 00 20 | 0...|..O.... |
|000017e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000017f0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001800| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001810| 20 20 20 20 20 20 20 20 | 20 20 20 35 0d 0b 00 49 | | 5...I|
|00001820| 6e 63 6f 72 72 65 63 74 | 2e 20 20 54 68 65 20 63 |ncorrect|. The c|
|00001830| 72 69 74 69 63 61 6c 20 | 6e 75 6d 62 65 72 73 20 |ritical |numbers |
|00001840| 61 72 65 20 11 33 78 20 | 11 31 3d 20 2d 31 2c 20 |are .3x |.1= -1, |
|00001850| 11 33 78 20 11 31 3d 20 | 31 2c 20 61 6e 64 20 11 |.3x .1= |1, and .|
|00001860| 33 78 20 11 31 3d 20 11 | 34 32 11 31 2e 20 20 54 |3x .1= .|42.1. T|
|00001870| 65 73 74 69 6e 67 0d 0b | 00 20 20 20 20 20 20 20 |esting..|. |
|00001880| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001890| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000018a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000018b0| 20 20 20 20 20 32 0d 0b | 00 20 20 20 20 20 20 20 | 2..|. |
|000018c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000018d0| 20 20 20 20 20 20 20 20 | 20 20 11 34 28 20 20 20 | | .4( |
|000018e0| 20 29 20 20 20 20 20 20 | 28 20 20 20 20 29 0d 0b | ) |( )..|
|000018f0| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |. | |
|00001900| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
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|00001920| 20 20 21 11 31 35 20 20 | 20 11 34 21 0d 0b 00 11 | !.15 | .4!....|
|00001930| 31 74 68 65 20 69 6e 74 | 65 72 76 61 6c 73 20 28 |1the int|ervals (|
|00001940| 2d 11 34 38 11 31 2c 20 | 2d 31 29 2c 20 28 2d 31 |-.48.1, |-1), (-1|
|00001950| 2c 20 31 29 2c 20 11 34 | 21 11 31 31 2c 20 11 34 |, 1), .4|!.11, .4|
|00001960| 32 21 11 31 2c 20 61 6e | 64 20 11 34 21 32 11 31 |2!.1, an|d .4!2.1|
|00001970| 2c 20 11 34 38 21 11 31 | 2c 20 77 65 20 67 65 74 |, .48!.1|, we get|
|00001980| 20 0d 0b 00 20 20 20 20 | 20 20 20 20 20 20 20 20 | ... | |
|00001990| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000019a0| 20 20 20 20 20 11 34 21 | 20 20 20 11 31 32 11 34 | .4!| .12.4|
|000019b0| 21 20 20 20 20 20 20 21 | 11 31 32 20 20 20 11 34 |! !|.12 .4|
|000019c0| 21 0d 0b 00 20 20 20 20 | 20 20 20 20 20 20 28 20 |!... | ( |
|000019d0| 20 20 20 29 20 20 20 20 | 20 20 20 20 20 20 20 20 | ) | |
|000019e0| 20 20 20 20 20 39 20 20 | 20 20 30 20 20 20 20 20 | 9 | 0 |
|000019f0| 20 39 20 20 20 20 30 0d | 0b 00 20 20 20 20 20 20 | 9 0.|.. |
|00001a00| 20 20 20 20 21 11 31 35 | 20 20 20 11 34 21 0d 0b | !.15| .4!..|
|00001a10| 00 11 31 5b 2d 31 2c 20 | 31 29 20 11 34 75 20 21 |..1[-1, |1) .4u !|
|00001a20| 32 11 31 2c 20 11 34 38 | 21 20 11 31 2e 0d 0b 00 |2.1, .48|! .1....|
|00001a30| 20 20 20 20 20 20 20 20 | 20 20 11 34 21 11 31 32 | | .4!.12|
|00001a40| 20 20 20 11 34 21 0d 0b | 00 20 20 20 20 20 20 20 | .4!..|. |
|00001a50| 20 20 20 39 20 20 20 20 | 30 0d 0a 00 00 17 4f 03 | 9 |0.....O.|
|00001a60| 0d 0b 00 53 6f 72 72 79 | 2c 20 6f 6e 65 20 6f 66 |...Sorry|, one of|
|00001a70| 20 74 68 65 73 65 20 61 | 6e 73 77 65 72 73 20 69 | these a|nswers i|
|00001a80| 73 20 63 6f 72 72 65 63 | 74 2e 20 20 54 72 79 20 |s correc|t. Try |
|00001a90| 61 67 61 69 6e 2e 0d 0a | 00 00 17 4f 03 0d 0b 00 |again...|...O....|
|00001aa0| 43 6f 72 72 65 63 74 2e | 20 20 54 68 65 20 64 6f |Correct.| The do|
|00001ab0| 6d 61 69 6e 20 6f 66 20 | 11 33 78 20 11 31 69 6e |main of |.3x .1in|
|00001ac0| 20 74 68 65 20 65 78 70 | 72 65 73 73 69 6f 6e 20 | the exp|ression |
|00001ad0| 69 73 20 61 6c 6c 20 72 | 65 61 6c 20 6e 75 6d 62 |is all r|eal numb|
|00001ae0| 65 72 73 2e 0d 0a 00 00 | 17 4f 09 20 20 20 20 20 |ers.....|.O. |
|00001af0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001b00| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001b10| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001b20| 20 20 20 20 20 20 20 20 | 20 20 20 11 32 32 0d 0b | | .22..|
|00001b30| 00 11 31 4e 6f 2e 20 20 | 53 69 6e 63 65 20 74 68 |..1No. |Since th|
|00001b40| 65 20 65 78 70 72 65 73 | 73 69 6f 6e 20 69 73 20 |e expres|sion is |
|00001b50| 64 65 66 69 6e 65 64 20 | 28 68 61 73 20 72 65 61 |defined |(has rea|
|00001b60| 6c 20 76 61 6c 75 65 73 | 29 20 6f 6e 6c 79 20 69 |l values|) only i|
|00001b70| 66 20 11 33 78 20 20 11 | 31 2d 20 33 11 33 78 20 |f .3x .|1- 3.3x |
|00001b80| 11 31 2b 20 33 0d 0a 00 | 20 20 20 20 20 20 20 20 |.1+ 3...| |
|00001b90| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001ba0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001bb0| 20 20 20 20 20 11 32 32 | 0d 0b 00 11 31 69 73 20 | .22|....1is |
|00001bc0| 6e 6f 6e 6e 65 67 61 74 | 69 76 65 2c 20 74 68 65 |nonnegat|ive, the|
|00001bd0| 20 64 6f 6d 61 69 6e 20 | 6f 66 20 11 33 78 20 11 | domain |of .3x .|
|00001be0| 31 69 73 20 67 69 76 65 | 6e 20 62 79 20 11 33 78 |1is give|n by .3x|
|00001bf0| 20 20 11 31 2d 20 33 11 | 33 78 20 11 31 2b 20 33 | .1- 3.|3x .1+ 3|
|00001c00| 20 11 34 3e 20 11 31 30 | 2e 20 20 53 69 6e 63 65 | .4> .10|. Since|
|00001c10| 20 74 68 65 20 0d 0a 00 | 20 20 20 20 20 20 20 20 | the ...| |
|00001c20| 20 20 20 20 20 20 20 20 | 20 11 32 32 0d 0b 00 11 | | .22....|
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|00001c40| 33 29 20 20 2d 20 34 28 | 31 29 28 33 29 20 3d 20 |3) - 4(|1)(3) = |
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|00002540| 20 20 20 11 34 44 32 32 | 20 20 20 20 20 20 20 20 | .4D22| |
|00002550| 20 20 20 20 20 44 32 32 | 0d 0b 00 20 20 20 20 20 | D22|... |
|00002560| 20 20 20 11 33 78 20 20 | 11 31 3e 20 31 36 20 20 | .3x |.1> 16 |
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|00002590| 20 20 11 33 78 20 11 31 | 3e 20 11 34 53 20 11 31 | .3x .1|> .4S .1|
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|000025b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 11 33 78 | | .3x|
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|00002600| 2d 34 29 2c 20 28 2d 34 | 2c 20 34 29 2c 20 61 6e |-4), (-4|, 4), an|
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|000026a0| 69 65 73 0d 0a 00 0d 0a | 00 0d 0b 00 20 20 20 20 |ies.....|.... |
|000026b0| 0e 78 31 2d 38 2d 31 0e | 54 75 74 6f 72 69 61 6c |.x1-8-1.|Tutorial|
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|000026f0| 20 20 0e 78 31 2d 38 2d | 33 0e 54 75 74 6f 72 69 | .x1-8-|3.Tutori|
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|00002710| 20 20 20 0e 78 31 2d 38 | 2d 34 0e 54 75 74 6f 72 | .x1-8|-4.Tutor|
|00002720| 69 61 6c 20 45 78 65 72 | 63 69 73 65 20 20 34 0f |ial Exer|cise 4.|
|00002730| 20 20 20 20 0e 78 31 2d | 38 2d 35 0e 54 75 74 6f | .x1-|8-5.Tuto|
|00002740| 72 69 61 6c 20 45 78 65 | 72 63 69 73 65 20 35 0f |rial Exe|rcise 5.|
|00002750| 0d 0a 00 0d 0b 00 20 20 | 20 20 20 20 20 20 20 20 |...... | |
|00002760| 20 20 20 20 20 20 20 20 | 20 0e 78 31 2d 38 2d 36 | | .x1-8-6|
|00002770| 0e 54 75 74 6f 72 69 61 | 6c 20 45 78 65 72 63 69 |.Tutoria|l Exerci|
|00002780| 73 65 20 20 36 0f 0d 0a | 00 0d 0b 00 20 20 20 20 |se 6...|.... |
|00002790| 0e 78 31 2d 38 2d 37 0e | 54 75 74 6f 72 69 61 6c |.x1-8-7.|Tutorial|
|000027a0| 20 45 78 65 72 63 69 73 | 65 20 20 37 0f 0d 0a 00 | Exercis|e 7....|
|000027b0| 0d 0b 00 20 20 20 20 0e | 78 31 2d 38 2d 38 0e 54 |... .|x1-8-8.T|
|000027c0| 75 74 6f 72 69 61 6c 20 | 45 78 65 72 63 69 73 65 |utorial |Exercise|
|000027d0| 20 20 38 0f 0d 0a 00 0d | 0b 00 20 20 20 20 0e 78 | 8.....|.. .x|
|000027e0| 31 2d 38 2d 39 0e 54 75 | 74 6f 72 69 61 6c 20 45 |1-8-9.Tu|torial E|
|000027f0| 78 65 72 63 69 73 65 20 | 20 39 0f 0d 0a 00 53 65 |xercise | 9....Se|
|00002800| 63 74 69 6f 6e 20 31 2e | 38 20 20 4f 74 68 65 72 |ction 1.|8 Other|
|00002810| 20 54 79 70 65 73 20 6f | 66 20 49 6e 65 71 75 61 | Types o|f Inequa|
|00002820| 6c 69 74 69 65 73 0d 0b | 00 20 20 20 20 20 20 20 |lities..|. |
|00002830| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002840| 20 20 20 20 11 32 32 0d | 0b 00 20 11 31 31 2e 20 | .22.|.. .11. |
|00002850| 20 53 6f 6c 76 65 20 74 | 68 65 20 69 6e 65 71 75 | Solve t|he inequ|
|00002860| 61 6c 69 74 79 20 11 33 | 78 20 20 11 31 3e 20 31 |ality .3|x .1> 1|
|00002870| 36 20 61 6e 64 20 67 69 | 76 65 20 74 68 65 20 61 |6 and gi|ve the a|
|00002880| 6e 73 77 65 72 20 69 6e | 20 69 6e 74 65 72 76 61 |nswer in| interva|
|00002890| 6c 20 6e 6f 74 61 74 69 | 6f 6e 2e 0d 0a 00 0d 0a |l notati|on......|
|000028a0| 00 20 20 20 20 20 0e 61 | 32 2d 38 2d 33 61 0e 28 |. .a|2-8-3a.(|
|000028b0| 61 29 0f 20 28 2d 11 34 | 38 11 31 2c 20 2d 34 29 |a). (-.4|8.1, -4)|
|000028c0| 2c 20 28 34 2c 20 11 34 | 38 11 31 29 20 20 20 20 |, (4, .4|8.1) |
|000028d0| 20 20 20 20 20 20 20 20 | 20 20 0e 61 32 2d 38 2d | | .a2-8-|
|000028e0| 33 62 0e 28 62 29 0f 20 | 28 2d 34 2c 20 34 29 0d |3b.(b). |(-4, 4).|
|000028f0| 0a 00 0d 0b 00 20 20 20 | 20 20 0e 61 32 2d 38 2d |..... | .a2-8-|
|00002900| 33 63 0e 28 63 29 0f 20 | 28 2d 11 34 38 11 31 2c |3c.(c). |(-.48.1,|
|00002910| 20 2d 34 5d 2c 20 5b 34 | 2c 20 11 34 38 11 31 29 | -4], [4|, .48.1)|
|00002920| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 0e 61 | | .a|
|00002930| 32 2d 38 2d 33 64 0e 28 | 64 29 0f 20 28 34 2c 20 |2-8-3d.(|d). (4, |
|00002940| 11 34 38 11 31 29 0d 0a | 00 0d 0a 00 59 6f 75 20 |.48.1)..|....You |
|00002950| 6d 61 79 20 77 61 6e 74 | 20 74 6f 20 72 65 76 69 |may want| to revi|
|00002960| 65 77 20 10 31 2d 38 2d | 32 0e 65 31 2d 38 2d 31 |ew .1-8-|2.e1-8-1|
|00002970| 0e 47 75 69 64 65 64 20 | 45 78 61 6d 70 6c 65 20 |.Guided |Example |
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|00002990| 38 20 20 4f 74 68 65 72 | 20 54 79 70 65 73 20 6f |8 Other| Types o|
|000029a0| 66 20 49 6e 65 71 75 61 | 6c 69 74 69 65 73 20 20 |f Inequa|lities |
|000029b0| 20 20 20 20 20 20 20 20 | 20 20 11 32 32 0d 0b 00 | | .22...|
|000029c0| 20 11 31 32 2e 20 20 53 | 6f 6c 76 65 20 11 33 78 | .12. S|olve .3x|
|000029d0| 20 20 11 31 2b 20 32 11 | 33 78 20 11 31 2b 20 31 | .1+ 2.|3x .1+ 1|
|000029e0| 20 11 34 3e 20 11 31 30 | 20 61 6e 64 20 67 69 76 | .4> .10| and giv|
|000029f0| 65 20 74 68 65 20 61 6e | 73 77 65 72 20 69 6e 20 |e the an|swer in |
|00002a00| 69 6e 74 65 72 76 61 6c | 20 6e 6f 74 61 74 69 6f |interval| notatio|
|00002a10| 6e 2e 0d 0a 00 0d 0a 00 | 20 20 20 20 20 0e 32 2d |n.......| .2-|
|00002a20| 38 2d 37 61 0e 28 61 29 | 0f 20 28 2d 11 34 38 11 |8-7a.(a)|. (-.48.|
|00002a30| 31 2c 20 11 34 38 11 31 | 29 20 20 20 20 20 20 20 |1, .48.1|) |
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|00002a50| 20 0e 32 2d 38 2d 37 62 | 0e 28 62 29 0f 20 28 2d | .2-8-7b|.(b). (-|
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|00003050| 20 20 20 20 20 20 20 20 | 20 32 20 20 20 20 20 20 | | 2 |
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+--------+-------------------------+-------------------------+--------+--------+
