MATH | MATHREVIEWS.CA v iote 0Reitt 1 000 Forpmore information visi.t Tutorial Class Instructor: John O'Reilly Max/Min Word Problems: 1. A farmer has 1000 metres of wooden fencing, and she wishes to fence off a rectangular plot of land bordered by a river, so that she does not require fencing on the side of the rectangle adjacent to the water. Find the dimensions of the rectangular plot with the greatest possible area. ANS: Dimensions 500 m by 250 m 2, A rectangular field is to be fenced on all four sides and then divided into two fields with a fence parallel to two opposite sides. If the total fencing available is 200m, what dimensions will give the maximum enclosed area? ANS: Dimensions lgo m by 50m 3. A closed box with a square base is to have a volume of 10 m®. The base cost $4/m?, the sides cost $2/m? and the top cost $1/m*. What dimensions will give the minimum cost to build the box? ANS: Dimensions 2mx 2mx 5/2 m 4. A manufacturer wishes to design an open box having a square base and a surface area of 108 square metres. What dimensions will a box be of maximum volume? ANS: 6mx 6m x 3m Evaluate each of the following limits (L'Hopital's Rule): In(sec 2x) ] 1 1 i VRS ANS: 2 6. mum({L--17) ans: 1 p AN . xX-1 . 2. lm(% ANS: 1 7. mi ANS: 0 5. g A0x) ANS: 0 8. liml=C0S'X ang: 3 xw X2 = 0 sin'*x = 2 4. lim(1-2x0" Ans: L 9. 1im&3% ANS: In3 " x~0 e3> _ e 3% ) 1-x+Inx . 1
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