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Unformatted text preview: Version 093 – Exam 1 – gualdani – (56455) 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 = 2 2. limit = 9 3. limit does not exist correct 4. limit = 5 5. limit = 7 Explanation: From the graph it is clear the f has a left hand limit at x = 2 which is equal to 9; and a right hand limit which is equal to 6. 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 = − 5 2. limit = − 6 3. limit = − 2 4. limit = − 4 correct 5. limit = − 3 6. limit does not exist Explanation: The left 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 − 3 x − 7 . Consequently, limit = 3 × 1 − 7 = − 4 . 003 10.0 points Determine lim x → 8 x − 8 √ x + 1 − 3 . 1. limit = 1 6 2. limit doesn’t exist 3. limit = 6 correct 4. limit = 3 5. limit = 1 3 Version 093 – Exam 1 – gualdani – (56455) 2 Explanation: After rationalizing the denominator we see that 1 √ x + 1 − 3 = √ x + 1 + 3 ( x + 1) − 9 = √ x + 1 + 3 x − 8 . Thus x − 8 √ x + 1 − 3 = √ x + 1 + 3 for all x negationslash = 8. Consequently, limit = lim x → 8 ( √ x + 1 + 3) = 6 . 004 10.0 points Determine lim h → f (1 + h ) − f (1) h when f ( x ) = 5 x 2 + 4 x + 1 . 1. limit does not exist 2. limit = 15 3. limit = 14 correct 4. limit = 18 5. limit = 17 6. limit = 16 Explanation: Since f (1 + h ) − f (1) = 5(1 + h ) 2 + 4(1 + h ) + 1 − 10 = 14 h + 5 h 2 = h (14 + 5 h ) , we see that lim h → f (1 + h ) − f (1) h = lim h → h (14 + 5 h ) h . Consequently, limit = 14 . 005 10.0 points Determine if the limit lim x → sin 7 x 6 x exists, and if it does, find its value. 1. limit = 7 2. limit = 6 7 3. limit = 7 6 correct 4. limit = 6 5. limit doesn’t exist Explanation: Using the known limit: lim x → sin ax x = a , we see that lim x → sin 7 x 6 x = 7 6 . 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 ) = 4 t 2 − 5 t + 7 ....
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 Spring '10
 Gualdani
 Derivative, 8 FT, 6 feet, 5 ft, 6 ft, 7 ft

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