q3 - Honors Calc 1 MAC3472 3203 Freebie Quiz Q3 Prof. JLF...

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Honors Calc 1 MAC3472 3203 Freebie Quiz Q3 Prof. JLF King 14Apr2008 Note. This is an open brain, open HHA, closed book, quiz. Please fill in the blanks. Show no work; no partial credit. Please be sure to write expressions unambigu- ously e.g, the expression “1 /a + b ” should be bracketed either [1 /a ] + b or 1 / [ a + b ]. Be careful with negative signs! Q3: [ Note The given parameters are length F and posint N .] A farmer has F feet of fencing with which he wishes to fence in a rectangular area, of some width w and depth d (for you to determine), and which is divided into N pens parallel to the width side. (So each pen has width w .) Let A N ( w ) denote the area of the big rectangle as a function of width. Compute this function: A N ( w ) = . Let w N and d N be the dimensions which maximize total area. Then w N = . Let α N denote the maximum area w N · d N Then lim N →∞ α N = . Q3:
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