document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=988780>Question 988780</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the definition of limit to verify that: \r<BR>\n" );
document.write( "\n" );
document.write( "(1). lim x->3 (5-2x) = - 1\r<BR>\n" );
document.write( "\n" );
document.write( "2). lim x->0 (4x+7) = 7 \r<BR>\n" );
document.write( "\n" );
document.write( "(3). lim x->7 (2x)/(x^2+1) = 1 \r<BR>\n" );
document.write( "\n" );
document.write( "Please explain how you solved.\r<BR>\n" );
document.write( "\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 #609258 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=609258\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \lim_{x\right{a}}\,f(x)\ =\ L\ \Leftrightarrow\ \forall\,\epsilon\,\in\,\mathbb{R}\,>\,0\,\exists\,\delta\,\in\,\mathbb{R}\,>\,0\,:\,0\,<\,|x\ -\ a|\,<\,\delta\,\Rightarrow\,|f(x)\ -\ L|\,<\,\epsilon\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \lim_{x\right{3}}\,5\ -\ 2x\ =\ -1\ \Leftrightarrow\ \forall\,\epsilon\,\in\,\mathbb{R}\,>\,0\,\exists\,\delta\,\in\,\mathbb{R}\,>\,0\,:\,0\,<\,|x\ -\ 3|\,<\,\delta\,\Rightarrow\,|5\ -\ 2x\ -\ (-1)|\,<\,\epsilon\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ |5\ -\ 2x\ +\ 1|\ <\ \epsilon\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ -\epsilon\ <\ -2x\ +\ 6\ <\ \epsilon\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{\epsilon}{2}\ >\ x\ -\ 3\ >\ -\frac{\epsilon}{2}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ |x\ -\ 3|\ <\ \frac{\epsilon}{2}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Choose <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large\ \delta\ =\ \frac{\epsilon}{2}\">.  Then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large |x\ -\ 3|\ <\ \delta\"> whenever <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large |5\ -\ 2x\ -\ (-1)|\ <\ \epsilon\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );