document.write( "Question 1164031: Calculate each of the following. Your answer must be a number. No arithmetic operations are allowed in your answer. Please give 7 places after your decimal point if you use scientific notation.
\n" ); document.write( "a) 940!/(30! 910!)=
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\n" ); document.write( "c) (518 ! - 514 !)/515 ! = \n" ); document.write( "

Algebra.Com's Answer #788326 by ikleyn(52802) $\"\"$ $\"About$

You can put this solution on YOUR website!
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Making calculations is the students' honor duty and a privilege !

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\n" ); document.write( "\n" ); document.write( "Below is my response to the Edwin's post.\r
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document.write( "Edwin, in your solution, you largely / widely use asymptotique formulas.\r\n" );
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document.write( "Asymptotics are not precise values, so you can not be sure and can not guarantee that your answer, \r\n" );
document.write( "obtained with the use of asymptotics, is valid PRECISELY.\r\n" );
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document.write( "Therefore, I select another way.\r\n" );
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document.write( "First, it is clear to everybody that we can cancel factors  910! in the numerator and the denominator. \r\n" );
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document.write( "We get then widely known expression for binomial coefficient \r\n" );
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document.write( "     = .\r\n" );
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document.write( "Next, it would be madness to calculate the products of 30 factors in the numerator and denominators SEPARATELY.\r\n" );
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document.write( "Instead, I will form the product of these 30 \"local\" ratios\r\n" );
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document.write( "    .\r\n" );
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document.write( "It is just VERY EASY to calculate it with Excel.  The product and the answer is\r\n" );
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document.write( "    3.6903095819*10^56.\r\n" );
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document.write( "    +-----------------------------------------------------------------+\r\n" );
document.write( "    |    It is really close to your result --- but using asymptotes,  | \r\n" );
document.write( "    |           you CAN NOT guarantee the precision,                  |\r\n" );
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document.write( "    |               while I CAN, using my method.                     |\r\n" );
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\n" ); document.write( "\n" ); document.write( "Edwin, I am very glad that you pointed/focused my attention on this calculation.\r
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\n" ); document.write( "\n" ); document.write( "I think, that it would be EXTREMELY USEFUL for students to see HOW I do it and to learn from me.\r
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\n" ); document.write( "\n" ); document.write( "Three points are key and are extremely important.\r
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document.write( "    (1)  Cancel all common factors in the numerator and denominator before going to massive calculations (!)\r\n" );
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document.write( "    (2)  Then present the ratio as the product of the small \"local\" ratios.\r\n" );
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document.write( "         Do not neglect it (!)  It is VERY IMPORTANT in such calculations (!)\r\n" );
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document.write( "    (3)  Do not use asymptotic formulas in these calculations : a) they are irrelevant, b) they do not provide\r\n" );
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document.write( "         the precise answer and c) they even do not guarantee the needed precision to you (!)\r\n" );
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\n" ); document.write( "\n" ); document.write( "And as a conclusion: This technique using these asymptotic formulas IS NOT ADEQUATE to the simplicity of the problem,\r
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\n" ); document.write( "\n" ); document.write( "and I am 179% sure that these students never heard, never learned and know NOTHING about them.\r
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\n" ); document.write( "\n" ); document.write( "Edwin, I worked for 40 years as a computer programmer - computational analyst - researcher, developing computer codes\r
\n" ); document.write( "\n" ); document.write( "and solving partial differential equations in 1D, 2D and 3D for heat transfer, thermal convection, radiation and hydrodynamics.\r
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\n" ); document.write( "\n" ); document.write( "All these years I was in the front line . . . \r
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\n" ); document.write( "\n" ); document.write( "So I know all the relevant theory and all the secrets and tricks in computational analysis (and all adjacent Mathematics).\r
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\n" ); document.write( "\n" ); document.write( "And even much more behind, aside and around it . . . \r
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\n" ); document.write( "\n" ); document.write( "So do not say please \" @ikleyn missed something. \"\r
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