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Unformatted text preview: Gauthier, Joseph – Homework 8 – Due: Oct 19 2007, 3:00 am – Inst: JEGilbert 1 This printout should have 14 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points Find the domain of the vector function r ( t ) = h t 4 , √ t 2 , ln(5 t ) i . 1. 2 < t ≤ 5 2. 2 < t < 5 3. 2 ≤ t < 5 correct 4. t < 2 , t > 5 5. 2 ≤ t ≤ 5 Explanation: A vector function r ( t ) = h f ( t ) , g ( t ) , h ( t ) i is defined when each of f ( t ) , g ( t ) and h ( t ) is defined. Now, for the given function, f ( t ) = t 4 is defined for all t while g ( t ) = √ t 2 is defined only when t ≥ 2. On the other hand, h ( t ) = ln(5 t ) is defined only 5 t > 0. Consequently, the domain of r ( t ) consists of all t , 2 ≤ t < 5 . keywords: vector function, domain, power function, square root function, log function, 002 (part 1 of 1) 10 points Find lim t → + r ( t ) when r ( t ) = h 8cos t, 7 e t , 8 t ln t i . 1. limit = h 8 , , 8 i 2. limit = h 8 , 7 , i correct 3. limit = h , 7 , i 4. limit = h 8 , , 8 i 5. limit = h 8 , 7 , 8 i Explanation: For a vector function r ( t ) = h f ( t ) , g ( t ) , h ( t ) i , the limit lim t → + r ( t ) = h lim t → + f ( t ) , lim t → + g ( t ) , lim t → + h ( t ) i . But for the given vector function, lim t → + f ( t ) = lim t → + 8cos t = 8 , while lim t → + g ( t ) = lim t → + 7 e t = 7 , and lim t → + h ( t ) = lim t → + t ln t = 0 , using L’Hospital’s Rule. Consequently, lim t → + r ( t ) = h 8 , 7 , i . keywords: vector function, limit, trig function log function, exponential function 003 (part 1 of 1) 10 points Gauthier, Joseph – Homework 8 – Due: Oct 19 2007, 3:00 am – Inst: JEGilbert 2 A space curve is shown in black on the surface x y z Which one of the following vector functions has this space curve as its graph?...
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 Fall '07
 Gilbert
 Derivative, Cos, vector function, Gauthier

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