Test 1 Solutions

# Test 1 Solutions - Solutions for Test C1 I a 5|h|2 < =)1/2...

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Solutions for Test C1 I: a) 5 | h | 2 < ε δ = ( ε 5 ) 1 / 2 b) First statement is false. Take a = - 2 and b = 1. Second statement is true. c) The expression is positive for all x < - 2 and all x > 1 since x 2 + x - 2 = ( x + 2)( x - 1) > 0 . d) ( x ) = 2( x - 2) + 1 = 2 x - 3 . e) ( x ) = ( x - 2) + 1 = x - 1 . II: a) Limit is 4 / 3 b) Limit is 3 / 2 c) Limit is 1 / 2 d) Limit is 0 e) Limit does not exist, since the limit from the right yields +1 and the limit from the left yields - 1. III: a) For all values of x . b) g ( h ) = | 8 + h | (5 + p 9 + (4 + h ) 2 ) p 9 + (4 + h ) 2 c) One reasonable answer to this problem is as follows. For | h | < 1 g ( h ) < 9 (5 + 9 + 3 2 ) 9 + 3 2 = 3 (5 + 3 2) 2 Hence for | h | < min(1 , (5 + 3 2) 2 3 ε

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Test 1 Solutions - Solutions for Test C1 I a 5|h|2 < =)1/2...

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