document.write( "Question 1199202: This is a calculus question. Could you explain #16 on https://www.math.purdue.edu/php-scripts/courses/oldexams/serve_file.php?file=16200FE-F2021.pdf which is about finding the limit using series? \n" ); document.write( "

Algebra.Com's Answer #832950 by ikleyn(52803) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "(1)  Write several starting terms of the first series\r\n" );
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document.write( "         cos(x) = 1 -  +  -  .\r\n" );
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document.write( "     Replace here x with , since you want  .  You will get\r\n" );
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document.write( "          = 1 -  +  - .           (1)\r\n" );
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document.write( "     You should keep as many terms of this series to have at least the term with .\r\n" );
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document.write( "(2)  Write several starting terms of the second series\r\n" );
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document.write( "          =  -  +  .\r\n" );
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document.write( "     Replace here x with , since you want  .  You will get\r\n" );
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document.write( "          =  -  + .          (2)\r\n" );
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document.write( "     You should keep as many terms of this series to have at least the term with .\r\n" );
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document.write( "(3)  Using (1) and (2), form    +  - .   You will get\r\n" );
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document.write( "          +  -  =  1 -  +  -  \r\n" );
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document.write( "                                             +   -  +  - 1 =\r\n" );
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document.write( "         = some terms will cancel; other will remain; I will keep the remaining terms with .  It gives \r\n" );
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document.write( "         = .   The other terms have x in degrees HIGHER than 12.\r\n" );
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document.write( "(4)  After dividing by ,  I have  plus other terms with x of degree higher than 1.\r\n" );
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document.write( "     When calculating the limit at x--> 0, these terms produce 0 (zero), so they are not interesting to me.\r\n" );
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document.write( "(5)  Thus I get the ANSWER:  the sough limit at  x --> 0  equals  .\r\n" );
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