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Unformatted text preview: Version 097 – Exam 1 – gualdani – (56410) 1 This printout should have 20 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Below is the graph of a function f . 2 4 6 − 2 − 4 − 6 2 4 6 8 − 2 − 4 Use the graph to determine lim x → 2 f ( x ) . 1. limit = 5 2. limit = 4 3. limit = 6 4. limit = 2 5. limit does not exist correct Explanation: From the graph it is clear the f has a left hand limit at x = 2 which is equal to 6; and a right hand limit which is equal to 4. Since the two numbers do not coincide, the limit does not exist . 002 10.0 points When f is the function defined by f ( x ) = braceleftbigg 3 x − 7 , x ≤ 1 , 5 x − 8 , x > 1 , determine if lim x → 1+ f ( x ) exists, and if it does, find its value. 1. limit does not exist 2. limit = − 3 correct 3. limit = − 2 4. limit = 0 5. limit = − 1 6. limit = − 4 Explanation: The right hand limit lim x → 1+ f ( x ) depends only on the values of f for x > 2. Thus lim x → 1+ f ( x ) = lim x → 1+ 5 x − 8 . Consequently, limit = 5 × 1 − 8 = − 3 . 003 10.0 points Determine lim x → 6 √ x + 3 − 3 x − 6 . 1. limit = 3 2. limit = 1 6 correct 3. limit = 6 4. limit doesn’t exist 5. limit = 1 3 Version 097 – Exam 1 – gualdani – (56410) 2 Explanation: After rationalizing the numerator we see that √ x + 3 − 3 = ( x + 3) − 9 √ x + 3 + 3 = x − 6 √ x + 3 + 3 . Thus √ x + 3 − 3 x − 6 = 1 √ x + 3 + 3 for all x negationslash = 6. Consequently, limit = lim x → 6 1 √ x + 3 + 3 = 1 6 . 004 10.0 points Determine lim h → f (1 + h ) − f (1) h when f ( x ) = 4 x 2 + 3 x + 5 . 1. limit does not exist 2. limit = 8 3. limit = 11 correct 4. limit = 10 5. limit = 9 6. limit = 7 Explanation: Since f (1 + h ) − f (1) = 4(1 + h ) 2 + 3(1 + h ) + 5 − 12 = 11 h + 4 h 2 = h (11 + 4 h ) , we see that lim h → f (1 + h ) − f (1) h = lim h → h (11 + 4 h ) h . Consequently, limit = 11 . 005 10.0 points Determine if the limit lim x → sin 6 x 7 x exists, and if it does, find its value. 1. limit = 7 2. limit = 6 7 correct 3. limit = 6 4. limit = 7 6 5. limit doesn’t exist Explanation: Using the known limit: lim x → sin ax x = a , we see that lim x → sin 6 x 7 x = 6 7 . 006 10.0 points After t seconds the displacement, s ( t ), of a particle moving rightwards along the xaxis is given (in feet) by s ( t ) = 2 t 2 − 2 t + 5 ....
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 Fall '09
 Gualdani
 Derivative, 5 feet, 4 ft, 5 ft, 6 ft, 7 ft

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