document.write( "Question 1196424: Consider the function f defined by f(x)=8x−3. Which quantities would need to be related to show that limx→1f(x)=5 using the formal definition of the limit?
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Algebra.Com's Answer #829248 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
Consider the function f defined by f(x)=8x−3. Which quantities
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document.write( "We must show that given any ε > 0 there exists δ such that \r\n" );
document.write( "whenever |x-1| < δ, then |(8x-3)-5| < ε.\r\n" );
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document.write( "Proof:\r\n" );
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document.write( "Suppose we are given ε > 0\r\n" );
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document.write( "|(8x-3)-5| < ε if and only if\r\n" );
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document.write( "|8x-3-5| < ε if and only if\r\n" );
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document.write( "|8x-8| < ε if and only if\r\n" );
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document.write( "|8(x-1)| < ε if and only if\r\n" );
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document.write( "8|x-1| < ε if and only if\r\n" );
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document.write( "|x-1| < ε/8 \r\n" );
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document.write( "So we take δ = ε/8.\r\n" );
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document.write( "We can stop here, but you can continue and say:\r\n" );
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document.write( "Now we have proved that if we take any ε > 0, then there exists\r\n" );
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document.write( "δ = ε/8 such that whenever\r\n" );
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document.write( "|x-1| < ε/8, then\r\n" );
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document.write( "8|x-1| < ε, then\r\n" );
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document.write( "|8(x-1)| < ε, then\r\n" );
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document.write( "|8x-8| < ε, then\r\n" );
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document.write( "|8x-3-5| < ε, then\r\n" );
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document.write( "|(8x-3)-5| < ε\r\n" );
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document.write( "But usually, you don't need to go through that second part if \r\n" );
document.write( "you will put \"if and only if\" between the steps of the first part \r\n" );
document.write( "as I did above.\r\n" );
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document.write( "Edwin
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