2.20 † Prove that if a(x) = |x|, the absolute value function, then a E C(R). (Use Exercise 1.9.) For reference: 1.9 † Prove: For all a and b in R, |la| – l6||

2.20<br>† Prove that if a(x) = |x|, the absolute value function, then a E C(R). (Use<br>Exercise 1.9.)<br>For reference:<br>1.9 † Prove: For all a and b in R,<br>|la| – l6|| < la – bl.<br>Intuitively, this says that la| and |b| cannot be farther apart than a and b are. (Hint:<br>Write |a| = |(a – b) + b| and use the triangle inequality. Then do the same thing for<br>|6|.)<br>

Extracted text: 2.20 † Prove that if a(x) = |x|, the absolute value function, then a E C(R). (Use Exercise 1.9.) For reference: 1.9 † Prove: For all a and b in R, |la| – l6|| < la="" –="" bl.="" intuitively,="" this="" says="" that="" la|="" and="" |b|="" cannot="" be="" farther="" apart="" than="" a="" and="" b="" are.="" (hint:="" write="" |a|="|(a" –="" b)="" +="" b|="" and="" use="" the="" triangle="" inequality.="" then="" do="" the="" same="" thing="" for="">

Jun 05, 2022

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2.20 † Prove that if a(x) = |x|, the absolute value function, then a E C(R). (Use Exercise 1.9.) For reference: 1.9 † Prove: For all a and b in R, |la| – l6||

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