2 December, 2013 Chapters 12—13 Review Math 1100 Name: The cluestiolls below are intended as a partial review. You should also refer to your written homework and quizzes (and, to a lesser extent. your \VebAssign work) as you study for the exam. 1. (a) What is an indefinite integral? ri- ae4_e -I F(x) o Sv&1 b—er , ,‘ , (b) What is a definite integral? T1- 21-e 01 P) tnta ctii t€j.t x 9v o kb i—i-i x) X—ctx,’.s L Ac C’ (c) How are definite integrals and indefinite integrals related? J@ F(x) ; {‘—- ,-kf,iI- w1i—eyAI ) -F() o1 h—e J f cb çcN cI II 0 ‘4 x k 9- •1< >< CD C” I•l r — H >(I “ + 3< >c 1 C C)) 0 CD CD E CD CD C)) crq CD CD CD Cl) LDI +I CD 0 0 — 1 )Cr3 CD -t P CD CD CD C.—, — )c• 0— .:z c____, ‘I - ‘<I D ‘— Izi I—’ 3 I’ “4 1 N - cr1 a-. + Hi 0 LJ - ‘I r r.j_ 0 > > (3 L _JI - 0 8 3. Find each area shown or described below. (a) The area enclosed by the curve y a; = = 2 + 1. the i-axis, and the lines x x and = z. ((z)-7 (;( ,)3 ) rzJ (b) The area enclosed by y number.) 2 I = —4x and the i-axis. (Your answer should be a positive 3 4x I’o I X Q 3 x d 10’) [((b)7 e —t t (o) x2iT’ -z 2 XLZZ = 2 —a; — 2x + 2. (Not pictured) (x-x - z) r) X’4—Zic 2 1 .L x —2 QY 0 r9 04-I 4-I -O (c) The area enclosed between y X’—Z (i- fo -(-I)J(()J a Li 4-cchans; () ((-I)z()’)J t.c ‘( L-??1i -t -A 3 K4-1xJ -l (t) c-’ •1 ( — t >( — r-) 1 + -t— r%) - N 1- r -I 1 ra N 7 -r —En C CD C CD CD CD CD + H II CD C C CD CD C C CD CD 0 CD 0 CD C CD CD CD CD CD 5. Suppose the marginal revenue for a product is MR = 900 and the marginal cost is MC = 3O/x + 4 with a fixed cost of $1000 (that is, it costs $1000 to produce 0 units). (a) How many units should be produced to maximize profit? d c q)o—3OJi oo_!crq oo 4- rej, - (ñ (ft): 9t2Ox- C ZO R() O ( 4 ff)Q.Q O oc 4 rq ( (b) What is the profit or loss from producing 5 units? 5i ,t IOC’ it 1000 /Z 3 () Zo /z 3 ) 1 ( ioD 1OfrC— L1C) ( a OK— ZO(xi) ui P(?cY (9 -‘- iO - qsO 3)2O. ,