NeXT Education Software Sampler 1992 Fall

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LaTeX Document | 1992-07-09 | 9.2 KB
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|00000c20| 74 3b 2f 4c 49 26 67 74 | 3b 0a 26 6c 74 3b 2f 4f |t;/LI&gt|;.&lt;/O|
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|00000c40| 26 67 74 3b 0a 26 6c 74 | 3b 2f 4c 49 26 67 74 3b |&gt;.&lt|;/LI&gt;|
|00000c50| 0a 26 6c 74 3b 4c 49 26 | 67 74 3b 28 32 2e 31 2e |.&lt;LI&|gt;(2.1.|
|00000c60| 33 36 29 20 20 53 65 65 | 20 46 69 67 75 72 65 20 |36)  See| Figure |
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|00000ce0| 53 55 50 26 67 74 3b 20 | 69 73 20 32 26 6c 74 3b |SUP&gt; |is 2&lt;|
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|00000d20| 2f 49 26 67 74 3b 20 3d | 20 26 6c 74 3b 49 26 67 |/I&gt; =| &lt;I&g|
|00000d30| 74 3b 78 26 6c 74 3b 2f | 49 26 67 74 3b 26 6c 74 |t;x&lt;/|I&gt;&lt|
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|00000d60| 74 3b 6d 26 6c 74 3b 2f | 49 26 67 74 3b 20 3d 20 |t;m&lt;/|I&gt; = |
|00000d70| 32 26 6c 74 3b 49 26 67 | 74 3b 78 26 6c 74 3b 2f |2&lt;I&g|t;x&lt;/|
|00000d80| 49 26 67 74 3b 26 6c 74 | 3b 53 55 42 26 67 74 3b |I&gt;&lt|;SUB&gt;|
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|00000da0| 53 69 6e 63 65 20 26 6c | 74 3b 21 26 6e 64 61 73 |Since &l|t;!&ndas|
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|00000de0| 3e 3c 53 55 42 3e 30 3c | 2f 53 55 42 3e 2c 20 3c |><SUB>0<|/SUB>, <|
|00000df0| 49 3e 78 3c 2f 49 3e 3c | 53 55 42 3e 30 3c 2f 53 |I>x</I><|SUB>0</S|
|00000e00| 55 42 3e 3c 53 55 50 3e | 32 3c 2f 53 55 50 3e 29 |UB><SUP>|2</SUP>)|
|00000e10| 0a 20 26 6e 64 61 73 68 | 3b 26 67 74 3b 0a 28 26 |. &ndash|;&gt;.(&|
|00000e20| 6c 74 3b 49 26 67 74 3b | 78 26 6c 74 3b 2f 49 26 |lt;I&gt;|x&lt;/I&|
|00000e30| 67 74 3b 26 6c 74 3b 53 | 55 42 26 67 74 3b 30 26 |gt;&lt;S|UB&gt;0&|
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|00000e60| 3b 26 6c 74 3b 53 55 42 | 26 67 74 3b 30 26 6c 74 |;&lt;SUB|&gt;0&lt|
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|00000e80| 26 67 74 3b 32 26 6c 74 | 3b 2f 53 55 50 26 67 74 |&gt;2&lt|;/SUP&gt|
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|00000eb0| 65 20 70 6f 69 6e 74 2d | 73 6c 6f 70 65 20 66 6f |e point-|slope fo|
|00000ec0| 72 6d 75 6c 61 20 67 69 | 76 65 73 20 74 68 65 20 |rmula gi|ves the |
|00000ed0| 74 61 6e 67 65 6e 74 20 | 6c 69 6e 65 20 61 73 20 |tangent |line as |
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|00000f20| 2d 3e 0a 3c 49 3e 79 3c | 2f 49 3e 20 2d 20 3c 49 |->.<I>y<|/I> - <I|
|00000f30| 3e 78 3c 2f 49 3e 3c 53 | 55 42 3e 30 3c 2f 53 55 |>x</I><S|UB>0</SU|
|00000f40| 42 3e 3c 53 55 50 3e 32 | 3c 2f 53 55 50 3e 20 3d |B><SUP>2|</SUP> =|
|00000f50| 20 32 3c 49 3e 78 3c 2f | 49 3e 3c 53 55 42 3e 30 | 2<I>x</|I><SUB>0|
|00000f60| 3c 2f 53 55 42 3e 28 3c | 49 3e 78 3c 2f 49 3e 20 |</SUB>(<|I>x</I> |
|00000f70| 2d 20 3c 49 3e 78 3c 2f | 49 3e 3c 53 55 42 3e 30 |- <I>x</|I><SUB>0|
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|00000fb0| 49 26 67 74 3b 78 26 6c | 74 3b 2f 49 26 67 74 3b |I&gt;x&l|t;/I&gt;|
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|00000fd0| 2f 53 55 42 26 67 74 3b | 26 6c 74 3b 53 55 50 26 |/SUB&gt;|&lt;SUP&|
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|00001010| 67 74 3b 30 26 6c 74 3b | 2f 53 55 42 26 67 74 3b |gt;0&lt;|/SUB&gt;|
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|000010d0| 2d 2d 3e 0a 3c 49 3e 78 | 3c 2f 49 3e 20 3d 20 3c |-->.<I>x|</I> = <|
|000010e0| 49 3e 78 3c 2f 49 3e 3c | 53 55 42 3e 31 3c 2f 53 |I>x</I><|SUB>1</S|
|000010f0| 55 42 3e 2c 20 3c 49 3e | 79 3c 2f 49 3e 20 3d 20 |UB>, <I>|y</I> = |
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|00001110| 6c 74 3b 49 26 67 74 3b | 78 26 6c 74 3b 2f 49 26 |lt;I&gt;|x&lt;/I&|
|00001120| 67 74 3b 20 3d 20 26 6c | 74 3b 49 26 67 74 3b 78 |gt; = &l|t;I&gt;x|
|00001130| 26 6c 74 3b 2f 49 26 67 | 74 3b 26 6c 74 3b 53 55 |&lt;/I&g|t;&lt;SU|
|00001140| 42 26 67 74 3b 31 26 6c | 74 3b 2f 53 55 42 26 67 |B&gt;1&l|t;/SUB&g|
|00001150| 74 3b 2c 20 26 6c 74 3b | 49 26 67 74 3b 79 26 6c |t;, &lt;|I&gt;y&l|
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|00001170| 20 26 6c 74 3b 21 26 6e | 64 61 73 68 3b 20 4d 41 | &lt;!&n|dash; MA|
|00001180| 54 48 0a 20 3c 21 2d 2d | 20 4d 41 54 48 0a 20 24 |TH. <!--| MATH. $|
|00001190| 30 20 20 2d 20 78 5f 30 | 5e 32 20 3d 20 32 20 78 |0  - x_0|^2 = 2 x|
|000011a0| 5f 30 20 28 20 78 5f 31 | 20 2d 20 78 5f 30 29 24 |_0 ( x_1| - x_0)$|
|000011b0| 0a 20 2d 2d 3e 0a 30 20 | 2d 20 3c 49 3e 78 3c 2f |. -->.0 |- <I>x</|
|000011c0| 49 3e 3c 53 55 42 3e 30 | 3c 2f 53 55 42 3e 3c 53 |I><SUB>0|</SUB><S|
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|000011f0| 42 3e 28 3c 49 3e 78 3c | 2f 49 3e 3c 53 55 42 3e |B>(<I>x<|/I><SUB>|
|00001200| 31 3c 2f 53 55 42 3e 20 | 2d 20 3c 49 3e 78 3c 2f |1</SUB> |- <I>x</|
|00001210| 49 3e 3c 53 55 42 3e 30 | 3c 2f 53 55 42 3e 29 0a |I><SUB>0|</SUB>).|
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|00001230| 20 26 6c 74 3b 49 26 67 | 74 3b 78 26 6c 74 3b 2f | &lt;I&g|t;x&lt;/|
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|00001290| 3b 53 55 42 26 67 74 3b | 30 26 6c 74 3b 2f 53 55 |;SUB&gt;|0&lt;/SU|
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|000013e0| 20 26 6c 74 3b 49 26 67 | 74 3b 78 26 6c 74 3b 2f | &lt;I&g|t;x&lt;/|
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|00001440| 26 67 74 3b 26 6c 74 3b | 41 20 49 44 3d 22 31 34 |&gt;&lt;|A ID="14|
|00001450| 22 26 67 74 3b 26 6c 74 | 3b 2f 41 26 67 74 3b 0a |"&gt;&lt|;/A&gt;.|
|00001460| 26 6c 74 3b 54 41 42 4c | 45 26 67 74 3b 0a 26 6c |&lt;TABL|E&gt;.&l|
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|00001480| 22 42 4f 54 54 4f 4d 22 | 26 67 74 3b 26 6c 74 3b |"BOTTOM"|&gt;&lt;|
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|000014a0| 3a 26 6c 74 3b 2f 53 54 | 52 4f 4e 47 26 67 74 3b |:&lt;/ST|RONG&gt;|
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|000014d0| 49 4f 4e 26 67 74 3b 0a | 26 6c 74 3b 54 52 26 67 |ION&gt;.|&lt;TR&g|
|000014e0| 74 3b 26 6c 74 3b 54 44 | 26 67 74 3b 26 6c 74 3b |t;&lt;TD|&gt;&lt;|
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|00001610| 6c 74 3b 2f 4c 49 26 67 | 74 3b 0a 26 6c 74 3b 4c |lt;/LI&g|t;.&lt;L|
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|00001630| 65 65 20 46 69 67 75 72 | 65 20 33 2e 20 20 53 6f |ee Figur|e 3.  So|
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|00001650| 68 65 20 77 61 79 3a 20 | 26 6c 74 3b 21 26 6e 64 |he way: |&lt;!&nd|
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|00001670| 4d 41 54 48 0a 20 24 6d | 20 3d 20 34 20 2d 20 32 |MATH. $m| = 4 - 2|
|00001680| 61 24 0a 20 2d 2d 3e 0a | 3c 49 3e 6d 3c 2f 49 3e |a$. -->.|<I>m</I>|
|00001690| 20 3d 20 34 20 2d 20 32 | 3c 49 3e 61 3c 2f 49 3e | = 4 - 2|<I>a</I>|
|000016a0| 0a 20 26 6e 64 61 73 68 | 3b 26 67 74 3b 0a 26 6c |. &ndash|;&gt;.&l|
|000016b0| 74 3b 49 26 67 74 3b 6d | 26 6c 74 3b 2f 49 26 67 |t;I&gt;m|&lt;/I&g|
|000016c0| 74 3b 20 3d 20 34 20 2d | 20 32 26 6c 74 3b 49 26 |t; = 4 -| 2&lt;I&|
|000016d0| 67 74 3b 61 26 6c 74 3b | 2f 49 26 67 74 3b 2c 20 |gt;a&lt;|/I&gt;, |
|000016e0| 74 61 6e 67 65 6e 74 20 | 6c 69 6e 65 20 69 73 20 |tangent |line is |
|000016f0| 26 6c 74 3b 21 26 6e 64 | 61 73 68 3b 20 4d 41 54 |&lt;!&nd|ash; MAT|
|00001700| 48 0a 20 3c 21 2d 2d 20 | 4d 41 54 48 0a 20 24 79 |H. <!-- |MATH. $y|
|00001710| 20 2d 20 28 34 61 20 2d | 20 61 5e 32 29 20 3d 20 | - (4a -| a^2) = |
|00001720| 28 34 20 2d 20 32 20 61 | 29 20 28 78 20 2d 20 61 |(4 - 2 a|) (x - a|
|00001730| 29 24 0a 20 2d 2d 3e 0a | 3c 49 3e 79 3c 2f 49 3e |)$. -->.|<I>y</I>|
|00001740| 20 2d 20 28 34 3c 49 3e | 61 3c 2f 49 3e 20 2d 20 | - (4<I>|a</I> - |
|00001750| 3c 49 3e 61 3c 2f 49 3e | 3c 53 55 50 3e 32 3c 2f |<I>a</I>|<SUP>2</|
|00001760| 53 55 50 3e 29 20 3d 20 | 28 34 20 2d 20 32 3c 49 |SUP>) = |(4 - 2<I|
|00001770| 3e 61 3c 2f 49 3e 29 28 | 3c 49 3e 78 3c 2f 49 3e |>a</I>)(|<I>x</I>|
|00001780| 20 2d 20 3c 49 3e 61 3c | 2f 49 3e 29 0a 20 26 6e | - <I>a<|/I>). &n|
|00001790| 64 61 73 68 3b 26 67 74 | 3b 0a 26 6c 74 3b 49 26 |dash;&gt|;.&lt;I&|
|000017a0| 67 74 3b 79 26 6c 74 3b | 2f 49 26 67 74 3b 20 2d |gt;y&lt;|/I&gt; -|
|000017b0| 20 28 34 26 6c 74 3b 49 | 26 67 74 3b 61 26 6c 74 | (4&lt;I|&gt;a&lt|
|000017c0| 3b 2f 49 26 67 74 3b 20 | 2d 20 26 6c 74 3b 49 26 |;/I&gt; |- &lt;I&|
|000017d0| 67 74 3b 61 26 6c 74 3b | 2f 49 26 67 74 3b 26 6c |gt;a&lt;|/I&gt;&l|
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