HW04-solutions

# HW04-solutions - handa(nh5757 HW04 meth(55830 This...

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handa (nh5757) – HW04 – meth – (55830) 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 10.0 points When f is defned by f ( x ) = x , fnd a so f ( a ) is two times the value oF f (3). 1. a = 9 4 2. a = 3 4 correct 3. a = 3 2 4. a = 3 5. a = 3 8 Explanation: ±irst we determine f ( a ) For a general value oF a . Now f ( a ) = lim x a f ( x ) f ( a ) x a . But when f ( x ) = x , f ( x ) f ( a ) x a = x a x a = x a ( x a )( x + a ) , aFter rationalizing the numerator. Thus f ( a ) = lim x a p 1 x + a P = 1 2 a . In this case f ( a ) = 2 f (3) = 1 2 a = 2 2 3 . Consequently, a = 3 (2) 2 = 3 4 . keywords: square root, defnition oF deriva- tive, limit 002 10.0 points ±ind the x -intercept oF the tangent line at the point P (3 , 1) on the graph oF f when lim h 0 f (3 + h ) 1 h = 4 . 1. x -intercept = 13 4 2. x -intercept = 11 3. x -intercept = 13 4. x -intercept = 11 5. x -intercept = 11 4 correct 6. x -intercept = 11 4 Explanation: Since lim h 0 f (3 + h ) f (3) h is the slope oF the tangent line at P (3 , 1) , an equation For this tangent line is y 1 = 4( x 3) , i.e. , y = 4 x 11 . Consequently, the x -intercept = 11 4 . 003 (part 1 of 3) 10.0 points

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handa (nh5757) – HW04 – meth – (55830) 2 A Calculus student leaves the RLM build- ing and walks in a straight line to the PCL Li- brary. His distance (in multiples of 40 yards) from RLM after t minutes is given by the graph 2 4 6 8 10 2 4 6 8 10 t distance
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## This note was uploaded on 11/21/2011 for the course M 408N taught by Professor Gualdini during the Spring '10 term at University of Texas.

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HW04-solutions - handa(nh5757 HW04 meth(55830 This...

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