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Unformatted text preview: Assignment 3 Solution 1. 000 , 20 000 , 20 ) 20000 ( 16 . 12 . ) ( > + + = x x x b x a x T i) We want ) ( lim = + x T x 12 . lim = + x a x ) ( 12 . = + a = a ii) 000 , 20 000 , 20 ) 20000 ( 16 . 12 . ) ( > + = x x x b x x T For T ( x ) to be continuous at x = 20,000 we must have: ) 000 , 20 ( ) ( lim ) ( lim 000 , 20 000 , 20 T x T x T x x = = + Now, 2400 ) 000 , 20 ( 12 . 12 . lim ) ( lim 000 , 20 000 , 20 = = = x x T x x b b x b x T x x = + = + = + ) 20000 20000 ( 16 . ) 20000 ( 16 . lim ) ( lim 000 , 20 000 , 20 2400 ) 000 , 20 ( 12 . 12 . lim ) 000 , 20 ( ) ( lim 000 , 20 000 , 20 = = = = x T x T x x So, b = 2400 and 000 , 20 000 , 20 ) 20000 ( 16 . 2400 12 . ) ( > + = x x x x x T Why is it important for these two conditions to hold? ) ( lim = + x T x tells us that people with very little to no income should be paying small amounts to no taxes. If a person has zero income, his/her taxes should be zero too. A person who makes 20,000 should not be exempted from taxes so T ( 20000 ) has to be defined. Secondly as income approaches 20, 000, the tax liability should be close to the tax liability for an...
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This note was uploaded on 09/13/2008 for the course MATH 1010u taught by Professor Kim during the Spring '08 term at Trinity University.
 Spring '08
 Kim
 Calculus

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