document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1020705>Question 1020705</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How to solve this limit?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lim%28x-%3E0%2C+++%28cos%282x%29+-+cos%28x%29%29%2F%280%29%29 ALIGN=MIDDLE  ALT=\"lim%28x-%3E0%2C+++%28cos%282x%29+-+cos%28x%29%29%2F%280%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Please explain<BR>\n" );
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 #636569 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=636569\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm assuming the original limit is<BR>\n" );
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document.write( "If so, then here are the steps\r<BR>\n" );
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document.write( "<tr><th>Step Number</th><th>Expression</th></tr>\r\n" );
document.write( "<tr><TD >1. </TD><TD ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lim%28x-%3E0%2C+++%28cos%282x%29+-+cos%28x%29%29%2F%28x%29%29 ALIGN=MIDDLE  ALT=\"lim%28x-%3E0%2C+++%28cos%282x%29+-+cos%28x%29%29%2F%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></tr>\r\n" );
document.write( "<tr><TD >2. </TD><TD ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lim%28x-%3E0%2C+++%282cos%5E2%28x%29+-+1+-+cos%28x%29%29%2F%28x%29%29 ALIGN=MIDDLE  ALT=\"lim%28x-%3E0%2C+++%282cos%5E2%28x%29+-+1+-+cos%28x%29%29%2F%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></tr>\r\n" );
document.write( "<tr><TD >3. </TD><TD ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lim%28x-%3E0%2C+++%282cos%5E2%28x%29+-+cos%28x%29+-+1%29%2F%28x%29%29 ALIGN=MIDDLE  ALT=\"lim%28x-%3E0%2C+++%282cos%5E2%28x%29+-+cos%28x%29+-+1%29%2F%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></tr>\r\n" );
document.write( "<tr><TD >4. </TD><TD ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lim%28x-%3E0%2C+++%28%282cos%28x%29%2B1%29%28cos%28x%29-1%29%29%2F%28x%29%29 ALIGN=MIDDLE  ALT=\"lim%28x-%3E0%2C+++%28%282cos%28x%29%2B1%29%28cos%28x%29-1%29%29%2F%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></tr>\r\n" );
document.write( "<tr><TD >5. </TD><TD ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lim%28x-%3E0%2C+++%282cos%28x%29%2B1%29%2A%28%28%28cos%28x%29-1%29%29%2F%28x%29%29%29 ALIGN=MIDDLE  ALT=\"lim%28x-%3E0%2C+++%282cos%28x%29%2B1%29%2A%28%28%28cos%28x%29-1%29%29%2F%28x%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></tr>\r\n" );
document.write( "<tr><TD >6. </TD><TD ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lim%28x-%3E0%2C+++%282cos%28x%29%2B1%29%29%2Alim%28x-%3E0%2C+++%28%28%28cos%28x%29-1%29%29%2F%28x%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></tr>\r\n" );
document.write( "<tr><TD >7. </TD><TD ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lim%28x-%3E0%2C+++%282cos%28x%29%2B1%29%29%2A0 ALIGN=MIDDLE  ALT=\"lim%28x-%3E0%2C+++%282cos%28x%29%2B1%29%29%2A0\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></tr>\r\n" );
document.write( "<tr><TD >8. </TD><TD ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Acos%280%29%2B1%29%2A0 ALIGN=MIDDLE  ALT=\"%282%2Acos%280%29%2B1%29%2A0\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></tr>\r\n" );
document.write( "<tr><TD >9. </TD><TD ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2A1%2B1%29%2A0 ALIGN=MIDDLE  ALT=\"%282%2A1%2B1%29%2A0\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></tr>\r\n" );
document.write( "<tr><TD >10. </TD><TD ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2B1%29%2A0 ALIGN=MIDDLE  ALT=\"%282%2B1%29%2A0\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></tr>\r\n" );
document.write( "<tr><TD >11. </TD><TD ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A0 ALIGN=MIDDLE  ALT=\"3%2A0\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></tr>\r\n" );
document.write( "<tr><TD >12. </TD><TD ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></tr>\r\n" );
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document.write( "------------------------------------------------<BR>\n" );
document.write( "Notes: \r<BR>\n" );
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document.write( "In step 2, I used the <a  rel=nofollow HREF= \"http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf\">trig identity</a> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%282x%29+=+2cos%5E2%28x%29-1 ALIGN=MIDDLE  ALT=\"cos%282x%29+=+2cos%5E2%28x%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > (see page 2 under \"Double Angle Formulas\")\r<BR>\n" );
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document.write( "In step 6, I broke up the limit using the limit law <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lim%28x-%3Ea%2C+++%28f%28x%29%2Ag%28x%29%29%29=lim%28x-%3Ea%2C+++%28f%28x%29%29%29%2Alim%28x-%3Ea%2C+++%28g%28x%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In step 7, I used the <a  rel=nofollow HREF= \"http://tutorial.math.lamar.edu/Classes/CalcI/ProofTrigDeriv.aspx\">special trig limit</a> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lim%28x-%3E0%2C+++%28%28cos%28x%29-1%29%2Fx%29%29+=+0 ALIGN=MIDDLE  ALT=\"lim%28x-%3E0%2C+++%28%28cos%28x%29-1%29%2Fx%29%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (scroll down to bottom half of the page)\r<BR>\n" );
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document.write( "From step 8 and beyond, I used the substitution rule and then evaluated/simplified to get the final answer of 0\r<BR>\n" );
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document.write( "So in the end, <BR>\n" );
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document.write( "Final Answer: <font color=red size = 5>0</font> </SPAN>\n" );
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