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Unformatted text preview: 422464224C01S02.035:To graphf(x) =√x2−9, note that there is no graph for−3< x <3, thatf(±3) = 0, andthatf(x)>0 forx <−3 and forx >3. Ifxis large positive, then√x2−9≈√x2=x, so the graph offhasxintercept (3,0) and rises asxincreases, nearly coinciding with the graph ofy=xforxlarge positive.The casex <−3 is trickier. In this case, ifxis a large negative number, thenf(x) =√x2−9≈√x2=−x(Note the minus sign!). So forx5−3, the graph offhasxintercept (−3,0) and, forxlarge negative,almost coincides with the graph ofy=−x. Later we will see that the graph offbecomes arbitrarily steepasxgets closer and closer to±3.C01S02.036:Asxincreases without bound—either positively or negatively—f(x) gets arbitrarily closeto zero. Moreover, ifxis large positive thenf(x) is negative and close to zero, so the graph offlies justbelow thexaxis for suchx. Similarly, the graph offlies just above thexaxis forxlarge negative. Ifxis slightly less than 1 but very close to 1, then...
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This note was uploaded on 09/14/2011 for the course MATH 101 taught by Professor Cheng during the Spring '11 term at Ecole Hôtelière de Lausanne.
 Spring '11
 CHENG
 Calculus

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