5 - Nguyen (ln4328) HW #5 treisman (54540) This print-out...

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Nguyen (ln4328) – HW #5 – treisman – (54540) 1 This print-out should have 15 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 10.0 points Suppose f is a continuous Function on [ 2 , 2] such that f ( 2) = 1 , f (2) = 1 . Which oF the properties below Follow with- out Further restriction on f by applying the Intermediate Value Theorem? A. f ( c ) = 0 For some c in ( 1 , 1); B. f ( x ) + 1 0 on ( 2 , 2); C. f 2 ( c ) = 1 4 For some c in ( 2 , 2). 1. B only 2. all oF them 3. C only correct 4. none oF them 5. B and C only 6. A and B only 7. A only 8. A and C only Explanation: The Intermediate Value Theorem (IVT) says: If f is continuous on an interval [ a, b ] , then for each N between f ( a ) and f ( b ) there exists c in ( a, b ) at which f ( c ) = N . Consequently, A. ±alse: f ( x ) = b 1 , 2 x < 1 3 2 x, 1 x 2 . B. ±alse: (choose any f so that f (0) = 2). C. True: (by IVT, f ( c ) = 1 2 For some c in ( 2 , 2)). 002 10.0 points IF a construction worker drops a wrench From the top oF a building 450 Feet high the wrench will be s ( t ) = 16 t 2 + 450 Feet above the ground aFter t seconds. Determine the velocity oF the wrench 4 sec- onds aFter it was was dropped. Correct answer: 128 Ft / sec. Explanation: The velocity oF the wrench is given by v ( t ) = lim h 0 s ( t + h ) s ( t ) h , so its velocity aFter a seconds is v ( a ) = lim h 0 s ( a + h ) s ( a ) h = ( 16( a + h ) 2 + 450) ( 16 a 2 + 450) h = 16 h (2 a + h ) h = 32 a . Thus v ( a ) = 32 a Ft/sec , the negative sign indicating that the wrench is Falling to the ground. At a = 4, thereFore, velocity = 128 Ft / sec Ft/sec . 003 10.0 points ±ind an equation For the tangent line at the point P (1 , f (1)) on the graph oF f when f is defned by f ( x ) = x 2 3 x + 4 .
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Nguyen (ln4328) – HW #5 – treisman – (54540) 2 1. y x + 5 = 0 2. y + x + 5 = 0 3. y + x 3 = 0 correct 4. y x 3 = 0 5. y + x 5 = 0 6. y x + 3 = 0 Explanation:
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5 - Nguyen (ln4328) HW #5 treisman (54540) This print-out...

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