document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1120558>Question 1120558</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider the function below. lim x -> 3 (2x+1)=7 <BR>\n" );
document.write( "What values of x guarantee that f(x)=2x+1 is within 0.54 units of 7? <BR>\n" );
document.write( "If x is within _____ units of 3, then f(x) is within 0.54 units of 7. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #736929 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=736929\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "We need to have<BR>\n" );
document.write( "7-0.54 < 2x+1 < 7+0.54<BR>\n" );
document.write( "6.46 < 2x+1 < 7.54<BR>\n" );
document.write( "5.46 < 2x < 6.54<BR>\n" );
document.write( "2.73 < x < 3.27<br><BR>\n" );
document.write( "Since this is a linear function, the upper and lower limits are the same distance of 0.27 from 3.<br><BR>\n" );
document.write( "So to guarantee that 2x+1 is within 0.54 units of 7, x has to be within 0.27 units of 3.<br><BR>\n" );
document.write( "The preceding is a formal process for finding the solution.  Since this is a linear function with a slope of 2, it should be obvious that x needs to be within 0.27 units of 3 for f(x) to be within 0.54 units of 7. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );