document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1067237>Question 1067237</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Not sure if this is the right section or not. <BR>\n" );
document.write( "Anyway, I'm struggling with Piecewise-defined functions. My question is about finding all the values of b that make the function continuous everywhere. \r<BR>\n" );
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document.write( "f(x)= (x^2-4)/x-2 x < 2, <BR>\n" );
document.write( "         [b-cos(pix/2)]^2. x >= 2 \r<BR>\n" );
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document.write( "Not sure how to solve it help would be great. I think I'm supposed to evaluate each at the limit as x approaches 2 but am not sure.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #683985 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=683985\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The only point you're concerned with is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > because the limit from the left must equal the limit from the right.<BR>\n" );
document.write( "So set the two functions equal to each other when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > to make it so.<BR>\n" );
document.write( "So,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-4%29%2F%28x-2%29=x%2B2 ALIGN=MIDDLE  ALT=\"%28x%5E2-4%29%2F%28x-2%29=x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > except when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2=b-cos%28%28pi%2F2%29x%29%29 ALIGN=MIDDLE  ALT=\"x%2B2=b-cos%28%28pi%2F2%29x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So now take the limit as x approaches 2,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2B2=b-cos%28%28pi%2F2%292%29 ALIGN=MIDDLE  ALT=\"2%2B2=b-cos%28%28pi%2F2%292%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4=b-cos%28pi%29 ALIGN=MIDDLE  ALT=\"4=b-cos%28pi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4=b-%28-1%29 ALIGN=MIDDLE  ALT=\"4=b-%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4=b%2B1 ALIGN=MIDDLE  ALT=\"4=b%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=3 ALIGN=MIDDLE  ALT=\"b=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=Fombitz&illustration_name=der1.JPG\">. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );