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Unformatted text preview: Version 071 – 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 → 4 f ( x ) . 1. limit does not exist correct 2. limit = 3 3. limit = 5 4. limit = 9 5. limit = 7 Explanation: From the graph it is clear the f has a left hand limit at x = 4 which is equal to 3; and a right hand limit which is equal to 1. 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 − 2 , x < 2 , 4 x − 3 , x ≥ 2 , determine if lim x → 2 − f ( x ) exists, and if it does, find its value. 1. limit = 6 2. limit = 2 3. limit = 5 4. limit = 4 correct 5. limit = 3 6. limit does not exist Explanation: The left hand limit lim x → 2 − f ( x ) depends only on the values of f for x > 2. Thus lim x → 2 − f ( x ) = lim x → 2 − 3 x − 2 . Consequently, limit = 3 × 2 − 2 = 4 . 003 10.0 points Determine lim x → 1 √ x + 3 − 2 x − 1 . 1. limit doesn’t exist 2. limit = 2 3. limit = 1 2 4. limit = 4 5. limit = 1 4 correct Version 071 – Exam 1 – gualdani – (56455) 2 Explanation: After rationalizing the numerator we see that √ x + 3 − 2 = ( x + 3) − 4 √ x + 3 + 2 = x − 1 √ x + 3 + 2 . Thus √ x + 3 − 2 x − 1 = 1 √ x + 3 + 2 for all x negationslash = 1. Consequently, limit = lim x → 1 1 √ x + 3 + 2 = 1 4 . 004 10.0 points Determine lim h → f (1 + h ) − f (1) h when f ( x ) = 2 x 2 + 5 x + 5 . 1. limit = 9 correct 2. limit = 11 3. limit = 8 4. limit does not exist 5. limit = 10 6. limit = 7 Explanation: Since f (1 + h ) − f (1) = 2(1 + h ) 2 + 5(1 + h ) + 5 − 12 = 9 h + 2 h 2 = h (9 + 2 h ) , we see that lim h → f (1 + h ) − f (1) h = lim h → h (9 + 2 h ) h . Consequently, limit = 9 . 005 10.0 points Determine if the limit lim x → sin 3 x 7 x exists, and if it does, find its value. 1. limit = 7 3 2. limit = 3 7 correct 3. limit doesn’t exist 4. limit = 7 5. limit = 3 Explanation: Using the known limit: lim x → sin ax x = a , we see that lim x → sin 3 x 7 x = 3 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 ) = 4 t 2 − 2 t + 5 ....
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This note was uploaded on 08/29/2010 for the course M 46455 taught by Professor Gualdani during the Spring '10 term at University of Texas at Austin.
 Spring '10
 Gualdani

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