FinalMakeup-001

Version 001 - Final Makeup - wolesensky - (KExams-F2019) 1 This print-out should have 28 questions. Multiple-choice questions may continue on the next column or page - find all choices before answering. 001 10.0points A car first speeds up, but then slows down. Sketch a graph of the position of the car as a function of time. 1. time position 2. time position 3. time position 4. time position 5. time position 6. time position 002 10.0points Below is the graph of a function f . 2 4 − 2 − 4 2 4 − 2 − 4

Version 001 - Final Makeup - wolesensky - (KExams-F2019) 2 Use the graph to determine lim x → 4 f ( x ). 1. limit = − 3 2. limit = − 1 3. limit = 0 4. limit = − 2 5. does not exist 003 10.0points Let F be the function defined by F ( x ) = x 2 − 4 | x − 2 | . Determine if the limit lim x → 2 + F ( x ) exists, and if it does, find its value. 1. limit = − 4 2. limit = 2 3. limit = − 2 4. limit = 4 5. limit does not exist 004 10.0points Determine if lim x → 0 √ 1 − x − √ 1 + x x exists, and if it does, find its value. 1. limit = 1 √ 2 2. limit = − 2 3. limit = − 1 4. limit = − 1 √ 2 5. limit = 2 6. limit does not exist 7. limit = 1 005 10.0points Determine where f ( x ) =      20 − x, x ≤ − 5, x 2 , − 5 < x < 2, 2 + x, x ≥ 2. is continuous, expressing your answer in in- terval notation. 1. ( −∞ , − 5) ∪ ( − 5 , 2) ∪ (2 , ∞ ) 2. ( −∞ , − 5) ∪ ( − 5 , ∞ ) 3. ( −∞ , ∞ ) 4. ( −∞ , 2) ∪ (2 , ∞ ) 5. ( −∞ , − 5) ∪ (2 , ∞ ) 006 10.0points Determine if lim x → −∞ parenleftbigg 2 x x − 1 + 5 x x + 1 parenrightbigg exists, and if it does, find its value. 1. limit = 7 2. limit does not exist 3. limit = 8 4. limit = 6

Version 001 - Final Makeup - wolesensky - (KExams-F2019) 3 5. limit = 10 6. limit = 9 007 10.0points If f is a differentiable function, then f ′ ( a ) is given by which of the following without further restriction on f ? A. lim h → 0 f ( a + h ) − f ( a ) h , B. lim x → a f ( x ) − f ( a ) x − a , C. lim x → a f ( x + h ) − f ( x ) h . 1. A only 2. A and C only 3. B only 4. A, B, and C 5. A and B only 008 10.0points If f is a function on ( − 2 , 2) whose graph is 1 2 − 1 − 2 1 2 − 1 − 2 which of the following is the graph of its derivative f ′ ? 1. 1 2 − 1 − 2 1 2 − 1 − 2 2. 1 2 − 1 − 2 1 2 − 1 − 2 3. 1 2 − 1 − 2 1 2 − 1 − 2 4. 1 2 − 1 − 2 1 2 − 1 − 2 5. 1 2 − 1 − 2 1 2 − 1 − 2