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Honors Precalculus Limits problem
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http://m.wolframalpha.XXX/XXXXX/?i=+%XXX%XXX-XX%XXX%5D%XX%XXX%5E2-1%XX+XXXX+-XX>x>10&x=XX&y=11</a><XX></p> <p>XXXX the vertical blue XXXX is XXXXXXX XXX asymptote XXX is XXX part XX the function.</p> <p><XX></p> <p>XXXX X:</p> <p>XX XXXXX this XX hand, you XXXXX XXXX to XXXXX XXXX XXX XXXXX</p> <p>Then you XXXX the rough XXXXX XX XXX graph (XXXX is to say XXXX XXXXX XX a XXXXXXXX asymptote XX -1 and a horizontal XXXXXXXX XX 1</p> <p>Then you would compare it XX XXXXX functions, XXXX XXXX would most likely look XXXXXXX to something XXXX X/x</p> <p>XXXXXXX, XXXXX the XXXXXXXX XX XXXXXX side XX XXX asymptote</p> <p>As we come from XXX XXXX (values below -1, like -1.XX as we XXXXXXXXX XXXXX) the XXXXXXXX XX going to be positive because XXX numerator, x-X XX XXXXX XX XX negative, and XXX XXXXXXXXXXX, x+1 XX also XXXXX XX XX negatuve</p> <p>That XX XX XXX x-X where x&XX;X is negative</p> <p>and x+X XXXXX x<-1 XX negative</p> <p>so x-X / x+1 &XX;-1 is positive</p> <p><XX></p> <p>XXX XXXXXXXX XX the XXXXX:</p> <p>we XXXX that very XXXXX from -X XX X XXX XXXXXXXX is still XXXXXXXX</p> <p>XXX XX x=4, the XXXXXXXX XX 0</p> <p>because x-4 XX x=4 is 0</p> <p>XXX x-X is XXX-zero</p> <p>so the function is defined, XXX zero</p> <p>XX XXX XXXXXXXX XXXX cross from XXXXXXXX y XXXXXX to XXXXXXXX y XXXXXX at x=4</p> <p>XXX XXX XXXX XXXXXXXX, XXX XXXXX will be XXXXXXX XX X/x (XXXX is to XXX, a partial XXXXX)</p> <p><br></p><p><XX></p><p>Edit 3:</p><p>To XXXX points you would just XXXX a XXXXX table, in the XXXXXX XX XXXXXXXX</p><p>(x-X)/(x+X)<br></p><p>so XXXX -10 to XX you XXXXX XXXXXXXXX XXXX XXXXX(XXXX XX the high detail one)</p><table> <tbody><tr> <td>x</td> <td>y</td> </tr> <tr> <td>-XX</td> <td>1.555555556</td> </tr> <tr> <td>-9</td> <td>X.625</td> </tr> <tr> <td>-8</td> <td>X.XXXXXXXXX</td> </tr> <tr> <td>-7</td> <td>X.833333333</td> </tr> <tr> <td>-6</td> <td>X</td> </tr> <tr> <td>-5</td> <td>2.25</td> </tr> <tr> <td>-X</td> <td>2.666666667</td> </tr> <tr> <td>-X</td> <td>X.X</td> </tr> <tr> <td>-2</td> <td>6</td> </tr> <tr> <td>-1</td> <td>#XXX/0!</td> </tr> <tr> <td>0</td> <td>-X</td> </tr> <tr> <td>1</td> <td>-X.5</td> </tr> <tr> <td>X</td> <td>-0.666666667</td> </tr> <tr> <td>X</td> <td>-X.XX</td> </tr> <tr> <td>X</td> <td>X</td> </tr> <tr> <td>X</td> <td>0.XXXXXXXXX</td> </tr> <tr> <td>X</td> <td>0.285714286</td> </tr> <tr> <td>X</td> <td>X.XXX</td> </tr> <tr> <td>X</td> <td>X.444444444</td> </tr> <tr> <td>9</td> <td>0.X</td> </tr> <tr> <td>XX</td> <td>0.XXXXXXXXX</td> </tr></tbody></table><p><XX></p> <p>Noting that XX x = -X is XXX vertical symptom</p><p><br></p><p>XX, XX XXXXX before, you know XXXX it looks XXXX XXXXXXX (XXXX X/x)</p><p>XXX XXXXXXX such XXXX at x=4 there XX the y=0</p><p>XXX that the vertical asymptote is at -X (because x=-X XXXXXXX in dividing by XXXX, so no XXXX XXXXX exists)</p><p>and XXX XXXXXXXXXX asymptote, because it XX a XXXXX XX 2 XXXXX order XXXXXXXXXXX, XX XXX XXXXX XX their co-efficients (x-X)/(x+X) where it is 1x / 1x in each case, so the XXXXXXXXXX asymptote XX XX y=X</p><p>So you can make a XXXXX XXXXX y=1 XX the horinstal portion, XXX x=-X XX XXX vertical portion</p><p>and the XXXXXXXX will be XX the top left, and bottom XXXXX XXXXXXXXX, with a shape XXXX XXXX of 1/x</p>">
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