Homework 5

# Homework 5 - vu (tv2894) Homework 5 (Quest) miner (55096)...

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vu (tv2894) – Homework 5 (Quest) – miner – (55096) 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 Four times the value oF f (1). 1. a = 1 16 correct 2. a = 1 32 3. a = 3 16 4. a = 1 8 5. a = 1 4 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 ) = 4 f (1) = 1 2 a = 4 2 1 . Consequently, a = 1 (4) 2 = 1 16 . keywords: square root, defnition oF deriva- tive, limit 002 10.0 points ±ind the y -intercept oF the tangent line at the point P (2 , 2) on the graph oF f when lim h 0 f (2 + h ) 2 h = 3 . 1. y -intercept = 4 3 2. y -intercept = 8 3. y -intercept = 4 4. y -intercept = 8 3 5. y -intercept = 4 3 6. y -intercept = 4 correct Explanation: Since lim h 0 f (2 + h ) f (2) h is the slope oF the tangent line at P (2 , 2) , an equation For this tangent line is y 2 = 3( x 2) , i.e. , y = 3 x 4 . Consequently, the y -intercept = 4 . 003 (part 1 oF 3) 10.0 points

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vu (tv2894) – Homework 5 (Quest) – miner – (55096) 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
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## This note was uploaded on 11/07/2010 for the course M 408N taught by Professor Gualdini during the Fall '10 term at University of Texas.

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Homework 5 - vu (tv2894) Homework 5 (Quest) miner (55096)...

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