Question

(12) Evaluate the following limits. You must show all your work to get full credit. 2.2 - 2-3 (a) lim 2-1 12-2-2 3.42 (b) lim 2-01 - COS 2 (c) lim x tan(3/2) 200 [8] Farmer Bob has 400 linear feet of fence with which to build a rectangular enclosure along the bank of a straight river. If no fence is required along the river bank, what dimensions will maximize the total area covered by the enclosure and what is the maximum area?

Answer 1

(12 a) lim 2xtx-3 x-1 x²-x-2 lim (x+1) (2x-3) x (1-2)(x+1) 28-3-201-3 lim x- x-2 S 3 -1-2 lim 2x²-x-3 s 3 X-1 x²-x-2 b) lim 3x2 x-0 1- Cosa = 3 lim x x->0 i-cosa We have an indetermineti form of type of we can apply L'ttopital's rule lim Cam) 33 x->0 d CI-CORN) da 2x - Glim k x-s0 Sina xoso sim we have an indeterminate foon of type af, we can apply L'topital's rule =3 lim Again lim e (ac) d. (sina) Copco x-so da 26 lim Cola 3 x² 2-30 l-casa a lim lim x'tan (3/2) tan (312) lam xosoo 1x bile have an indeterminite fom of type , we can apply L'topitals rule

- oo lim x -1/ser - lim da (tan (3/4)) -3 See) a ( 1 ) lim seir (3/2) =3 lim! - Cox (3/x) lim condition asoo ) -3 sao 3 lim cos (3/6) a-so = 3 = 3.7 i lim xetan ( 2 ) = 3 River 2 g Given that at&ty=400 ft y = 400-22 Area A(X) = 1; x) (y)=(x) (400-22) = 400X-222 To find manimum aree A'(a)=0 Al(&) = 400-48 - 400 - 4% -0 => 2 = 100 Then y= 400-2 (100) = 200 Maximum Area a ny=100 (206) A = 20000 ft i. The dimensions are 100 ft x zooft Maximum Area = 20000 ft²