HW02-solutions - handa(nh5757 HW02 meth(55830 This...

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handa (nh5757) – HW02 – meth – (55830) 1 This print-out should have 6 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0points Determine the value of lim x 2 f ( x ) + 2 g ( x ) 5 f ( x ) 6 g ( x ) when lim x 2 f ( x ) = 3 , lim x 2 g ( x ) = 4 . 1. limit = 5 9 2. limit = 5 39 correct 3. limit = 11 9 4. limit does not exist 5. limit = 11 39 Explanation: By properties of limits lim x 2 f ( x ) + 2 g ( x ) = lim x 2 f ( x ) + 2 lim x 2 g ( x ) = 5 while lim x 2 5 f ( x ) 6 g ( x ) = 5 lim x 2 f ( x ) 6 lim x 2 g ( x ) = 39 negationslash = 0 Consequently, by properties of limits again, lim x 2 f ( x ) + 2 g ( x ) 5 f ( x ) 6 g ( x ) = 5 39 . 002 10.0points Below are the graphs of functions f and g . 4 8 4 4 8 4 8 f : g : Use these graphs to determine lim x 8 { f ( x ) + g ( x ) } . 1. limit = 3 2. limit = 3 3. limit does not exist 4. limit = 7 5. limit = 1 correct Explanation: From the graph it is clear that lim x 8 { f ( x ) + g ( x ) } = 1 .
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