document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=380324>Question 380324</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi All, Please can someone help\r<BR>\n" );
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document.write( "Derive the Maclaurin series for sin x as<BR>\n" );
document.write( "sin x = x -x^3/3!+x^5/5! - ...\r<BR>\n" );
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document.write( "Hence write down the Maclaurin series for x sin x and sin 3x.\r<BR>\n" );
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document.write( "Thank You </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #269898 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=269898\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Note the definition of a power series\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+f%28c%29+%2B+%28f%5E%281%29%28c%29%2F1%21%29%28x+-+c%29+%2B+%28f%5E%282%29%28c%29%2F2%21%29%28x+-+c%29%5E2+%2B+... ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > (sorry, I can't put the f \"prime\" in without an error message being displayed)\r<BR>\n" );
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document.write( "If f(x) = sin x then its derivatives are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%281%29%28x%29+=+cos+x ALIGN=MIDDLE  ALT=\"f%5E%281%29%28x%29+=+cos+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%282%29%28x%29+=+-sin+x ALIGN=MIDDLE  ALT=\"f%5E%282%29%28x%29+=+-sin+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%283%29+%28x%29+=+-cos+x ALIGN=MIDDLE  ALT=\"f%5E%283%29+%28x%29+=+-cos+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%284%29+%28x%29+=+sin+x ALIGN=MIDDLE  ALT=\"f%5E%284%29+%28x%29+=+sin+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "etc.\r<BR>\n" );
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document.write( "The Maclaurin series is pretty much the same as a Taylor series except that it is centered around 0. Using the power series definition, we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+f%280%29+%2B+f%5E%281%29%280%29%28x%29+%2B+%28%28f%5E%282%29%280%29%29%2F2%21%29+%28x%5E2%29+%2B+%28%28f%5E%283%29%280%29%29%29%2F3%21+%2B+...%0D%0A%0D%0AGiven+that+f%280%29+=+0%2C+f%27%280%29+=+1%2C+etc.+%28from+taking+derivative+of+sine%29+we+have%0D%0A%0D%0A%7B%7B%7Bf%28x%29+=+sin+x+=+0+%2B+%281%2F1%21%29+%2B+%280%2F2%21%29%28x%5E2%29+-+%281%2F3%21%29+%28x%5E3%29+%2B+... ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+x+=+1+-+%281%2F3%29+%28x%5E3%29+%2B+%281%2F5%29+%28x%5E5%29+%2B+... ALIGN=MIDDLE  ALT=\"sin+x+=+1+-+%281%2F3%29+%28x%5E3%29+%2B+%281%2F5%29+%28x%5E5%29+%2B+...\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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