Test1s - MATH 1501 Test 1 September 14, 2009 No books or...

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MATH 1501 Test 1 September 14, 2009 No books or notes allowed. No laptop, graphic calculator or wireless devices allowed. Write clearly. Name: Question: 1 2 3 4 5 6 7 8 Total Points: 5 7 17 10 17 10 10 24 100 Score:
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MATH 1501 Test 1 September 14, 2009 1. (5 points) Find the domain of the following function: f ( x ) = 1 2 x + 1 Solution: We need x ≥ - 1 / 2 for 2 x + 1 to exist. But x ± = - 1 / 2 if not we havce a division by 0. So that we have: D ( f ) = ± - 1 2 , (1) 2. (7 points) Let f ( x ) be defined by: f ( x ) = ( x 2 - 1 for x < 3 2 ax for x 3 Find the values of a for which f is continuous. Solution: The function is clearly continuous for every x ± = 3. At x = 3 we have lim x 3 - f ( x ) = lim x 3 - ( x 2 - 1) = 8 (2) lim x 3 + f ( x ) = lim x 3 + (2 ax ) = 6 a (3) so that we need 6 a = 8 or a = 4 3 (4) Page 1 of 5
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MATH 1501 Test 1 September 14, 2009 3. Compute the indicated limits. (a) (7 points)
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Test1s - MATH 1501 Test 1 September 14, 2009 No books or...

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