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Exam1Winter11Sol

# Exam1Winter11Sol - Math 116 First Midterm February 2011...

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Math 116 / Exam 1 (February 2011) page 2 1 . [10 points] Indicate if each of the following statements are true or false by circling the correct answer. Justify your answers. a . [2 points] If F ( x ) is an antiderivative of an even function f ( x ), then F ( x ) must also be an even function. True False Solution: f ( x ) = 3 x 2 has F ( x ) = x 3 + 1 as an antiderivative which is not even (not odd either). b . [2 points] If G ( x ) is an antiderivative of g ( x ) and ( G ( x ) - F ( x )) 0 = 0, then F ( x ) is an antiderivative of g ( x ). True False Solution: g ( x ) = G 0 ( x ) = F 0 ( x ) hence F ( x ) is an antiderivative of g ( x ). c . [2 points] Let f ( t ) = bt + ct 2 with b > 0 and c > 0, then Left( n ) R 10 0 f ( t ) dt for all n .
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Exam1Winter11Sol - Math 116 First Midterm February 2011...

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