document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1179792>Question 1179792</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which combination of limit properties is required to evaluate this limit?\r<BR>\n" );
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document.write( "lim x-->4 (24/x-2x+2)^3\r<BR>\n" );
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document.write( "a. sum, difference, product, root<BR>\n" );
document.write( "b. sum, difference, product, power<BR>\n" );
document.write( "c. sum, difference, quotient, power <BR>\n" );
document.write( "d. sum, difference, quotient, root<BR>\n" );
document.write( "e. A limit does not exist. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850172 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850172\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To evaluate the limit:\r<BR>\n" );
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document.write( "lim (x→4) (24/x - 2x + 2)³\r<BR>\n" );
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document.write( "We need to break down the expression and apply the appropriate limit properties:\r<BR>\n" );
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document.write( "1.  **Quotient:** We have a term 24/x, which requires the quotient rule for limits.<BR>\n" );
document.write( "2.  **Difference:** We have terms (24/x) - 2x, which requires the difference rule for limits.<BR>\n" );
document.write( "3.  **Sum:** We have terms (24/x - 2x) + 2, which requires the sum rule for limits.<BR>\n" );
document.write( "4.  **Power:** The entire expression is raised to the power of 3, which requires the power rule for limits.\r<BR>\n" );
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document.write( "Therefore, the combination of limit properties required is:\r<BR>\n" );
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document.write( "* Sum<BR>\n" );
document.write( "* Difference<BR>\n" );
document.write( "* Quotient<BR>\n" );
document.write( "* Power\r<BR>\n" );
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document.write( "The correct answer is **c. sum, difference, quotient, power**.<BR>\n" );
document.write( " </SPAN>\n" );
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