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| Line 1: |
Line 1: |
| − | {| class="wikitable" style="clear:both; margin:0.5em auto; font-size:95%; border:1px solid black;"
| + | <asy> |
| − | | style="background:#ccf;text-align:center;" colspan="3" | '''[[{{{year}}} USAMO]]''' ('''[[{{{year}}} USAMO Problems|Problems]]''') • [http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=27&year={{{year}}} Resources])
| + | Label f; |
| − | |-
| + | f.p=fontsize(6); |
| − | | width="50%" align="center" rowspan="{{{rowsp|1}}}" | {{{beforetext|Preceded by<br/>}}}'''{{{before|[[{{{year}}} USAMO Problems/Problem {{{num-b}}}|Problem {{{num-b}}}]]}}}'''
| + | xaxis(1,3); |
| − | | width="50%" align="center" rowspan="{{{rowsf|1}}}" | {{{aftertext|Followed by<br/>}}}'''{{{after|[[{{{year}}} USAMO Problems/Problem {{{num-a}}}|Problem {{{num-a}}}]]}}}'''
| + | |
| − | |-
| + | real f(real x) |
| − | | colspan="3" style="text-align:center;" | [[{{{year}}} USAMO Problems/Problem 1|1]] '''•''' [[{{{year}}} USAMO Problems/Problem 2|2]] '''•''' [[{{{year}}} USAMO Problems/Problem 3|3]] '''•''' [[{{{year}}} USAMO Problems/Problem 4|4]] '''•''' [[{{{year}}} USAMO Problems/Problem 5|5]]
| + | { |
| − | |-
| + | return 0.2 * (x - 1)^2 + 0.5; |
| − | | colspan="3" style="text-align:center;" | '''[[USAMO Problems and Solutions | All USAMO Problems and Solutions]]'''
| + | } |
| − | |}
| + | draw(graph(f,1,3)); |
| | + | |
| | + | dot((1.5,0.55)); |
| | + | dot((2,0.7)); |
| | + | draw((1,0.4)--(3,1),dotted); |
| | + | draw((1,0.45)--(3,0.85),dotted); |
| | + | |
| | + | draw((1.5,0)--(1.5,1.5),dashed); |
| | + | draw((2,0)--(2,1.5),dashed); |
| | + | |
| | + | label("$f(x)$",(3,1.3),E); |
| | + | label("$x_0$",(1.5,-0.1),N); |
| | + | label("$x_0 + h$",(2,-0.1),N); |
| | + | </asy> |
![[asy] Label f; f.p=fontsize(6); xaxis(1,3); real f(real x) { return 0.2 * (x - 1)^2 + 0.5; } draw(graph(f,1,3)); dot((1.5,0.55)); dot((2,0.7)); draw((1,0.4)--(3,1),dotted); draw((1,0.45)--(3,0.85),dotted); draw((1.5,0)--(1.5,1.5),dashed); draw((2,0)--(2,1.5),dashed); label("$f(x)$",(3,1.3),E); label("$x_0$",(1.5,-0.1),N); label("$x_0 + h$",(2,-0.1),N); [/asy]](http://latex.artofproblemsolving.com/f/7/4/f74d9b7d72e4dd8283805d979a32fcab302e28f0.png)
