document.write( "Question 892661: Please help me out with this question:
\n" ); document.write( "How to find the oblique or curvilinear asymptotes for this function
\n" ); document.write( ". f(X)= (X^3-1)/(x^2-9)
\n" ); document.write( "Thanks :) \n" ); document.write( "

Algebra.Com's Answer #540692 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "To find vertical asymptotes, set the denominator = 0\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "; \r\n" );
document.write( ";   \r\n" );
document.write( "\r\n" );
document.write( "So the two vertical asymptotes are x=-3 and x=3.\r\n" );
document.write( "We draw those.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now we ind what you asked for, the oblique or curvilinear \r\n" );
document.write( "asymptotes.  To find that we use long division:\r\n" );
document.write( "\r\n" );
document.write( "                x+0 \r\n" );
document.write( "x²+0x-9)x³+0x²+0x-1\r\n" );
document.write( "        x³+0x²-9x\r\n" );
document.write( "           0x²+9x-1\r\n" );
document.write( "           0x²+0x+0\r\n" );
document.write( "               9x-1\r\n" );
document.write( "\r\n" );
document.write( "and we can rewrite the equation: \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "When x gets larger and larger in absolute value\r\n" );
document.write( "the fraction gets closer and closer to 0, so to \r\n" );
document.write( "get the asymptote we drop the fraction and set \r\n" );
document.write( "y = the quotient only.\r\n" );
document.write( "\r\n" );
document.write( "So we have an oblique asymptote, which has \r\n" );
document.write( "this equation: \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We draw it:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The we get some points\r\n" );
document.write( "\r\n" );
document.write( "x|-10| -7 |  -5  |-3.5 |-2.5|\r\n" );
document.write( "-|---|----|------|-----|-----\r\n" );
document.write( "y|-11|-8.6|-7.875|-13.5|6.05|\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "x| 10 | 7  |   5  | 4 | 2.6|\r\n" );
document.write( "-|----|----|------|---|-----\r\n" );
document.write( "y|10.9|8.55| 7.75 | 9 |-7.4|\r\n" );
document.write( "\r\n" );
document.write( "And sketch the graph:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "
\n" ); document.write( " \n" ); document.write( "

\n" );