- l g. (x- r2j - C - (a 6.t~)?,& Page 5 87 (43-46) .: (See your notes, qub, and test for this section). (hx + ly(27x7 + 2)- (92 + 2x)(3)(6x+lY(6) I

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1 Math 1303 Final Exam Review Chapters Factor each of the following completely: (hx + ly(27x7 + 2)- (92 + 2x)(3)(6x+lY(6) Page 5 87 (43-46),-% - l g (a 6.t~)?,& a. Rationalize the numerator: Page 594 (6 1-66) b. Rationalize the denomhator: Page 594 (49-54) (x- r2j - C - \ _-.: (See your notes, qub, and test for this section). +-' a. Write the equation of the whose endpoints are (3, -10) and

2 ., b. Write the equation of the line tangent to circle with center (6, -1) at the point i +& 1 m y s --v 4, Find the domain for each function shown. Write the domain in interval notation. Page 74 (43-48) Sketch the graph of = --)cs3

3 7. MmimizelMinimize: Page 92 (57 B,C; 58 B,C) 8. Break-Even Analysis: Page 92 (59 B; 60 B) - %'Sf '181 ae-c;r,w- A cable television firm prcscnty serves 5000 households and charges $20 per month. A marketing survey indicates that each decrease of $ l in the monthly charge will result in 500 new customers. k t RCx) denote the total monthly revenue when the monthly charge is x dollars. Find the vdue of x that results in the maximum monthly revenue. e: + huus )( ~L.arc- J i h d k ~ ~ - The marketing research department for a company that manufactures and sells "notebook" computers established the following Revenue and Cost Functions where x is thousands of computers and both C(x) and R(x) are in thousands of dulars. Both functions have domain 1 5 x Find the break-even points. x= - -b RcK'= (5000 +%DDX\ (20-x -2 RM= /ooooo -500 ux + / Q,oDOf-~oox~ 1-9. Cost, ~evenue, Profit functions; (See notes) A manufacturer has monthly fixed costs of $40,000 and a production cost of $8 for each item produced. The product sells for $12 each. Find a hnction for each of the following: a. Total Cost function b. fitat Revenue function c. Profit hction d. Number of units needed to break-even.

4 10. Difference Quotient: Page 61 ( part c only). Given f(x) = x - 1 and g(x) = x" 3x a. Find f (u + k) - f (a) b. Find R(x + h) - ~(1) /+k -4-'7 - CW-* h, - &+;wp" _f,""..c -, * Use a sign chart to help you determine the soution for each inequality: Page 11 (3-6; 19,2Q, 27,28,39,40) t:jw. S:,/a. >r+ 3 i 12. Graphing Rational Functions: (Read page 88 in text (Sec. 2.3) and see class notes)

5 For exercises 13, 14, and 15, solve each indicated equation. f you get a deci.mil answer, round to 3 decimal places. )O;,O=/ 13. ~xponent3 equations: Page 103 (43-52) 14. fioperties of Logarithms: Page 117 (53-58) Y7Q 3 - ~ ~ a. 2 log x = log 2 -- log (3x - 4) %>% 1 5. Change from log form 10 exponent fom and solve: Page (59,601 %7 + a. n (x -4)= 3 4 %70 b. log x + log (x - 3) = 1

6 16. Using exponential functions. The temperature of a cup of coffee f minutes after it is poured is given by T = OOe a a4461 where T is meawed in degrees Fahrenheit. a. What was the ternrnnture of the coffee when it was pmred? -- 0 b. when will the coffee be coo1 enough to &ink (120" F)? --o*f+lc 120-?U+ 100-e -, o rc GLt 5 = /Doe &[.<)= a s = e - 0 -, O QcCLt,&tl/g 5ik -, 0 ++LC - 0 4, 4 ip -, 0LCijL-t 17. Compound nterest and Continuous Compound nterest: Know the formulas! Page 147 (61-68) How long - will it tnke an investment of Y- n+ A= PCrt-) a. compounded = loo0 (/+'F 4t A = j,w1~85 &x, f'7. /dol) f #-;100fi Blakely nvestment Company owns and office building in the commercial district of a city. AJ a result of continued success of an urban renewal program, local business is enjoying a mushroom growth. The current market value of the property is $300,000. f the expected rate of inflation for the present market price is 10% per year, find how long it will take for the plow to be worth $500,000. P=~DDDDD ~ D ~ 0 0 O = 3 0, l. J ( / + ' ~ ~ ~

7 18. Solve the system. You may use whatever method you prefer. Page 185 (5-26) 19. Set up a system of equations and use whichever method you prefer to solve the problem. Page ,52,55A, 56A, 63,64E a. Find the equilibrium price and quantity, if the weekly demand and supply functions for Sportsman 5 x 7 tents are given by: Demand: p = -0. 1x2 - x i- 40 where p is the price measured in dollars, and Supply; p = 0. lx2 + 2x + 20 x is the quantity measured in hundreds of tents. 3, vl+b+a~ = -* 1.g -'(+4o L-- "CCCC n two accounts, The interest med on the accounts is 8% and 9% of $2,110 per year hm these accounts. How much is invested in each? yxtq = asooo

8 20. Systems of nequalities: Page 273 ( 17-26) Solve the system graphically. ndicate whether the solution Find the coordinates of all corner pints ''/4 z -72 dj h:b?+611 ion is bounded or un ounded. Ren i, ' 2 1. Linear Programming: Page 287 (3 A, 32A, 33A) * - x 1 too wd f.4:~ 30 A company makes 2 models of machines, model X and model Y. Each model X costs $100 to make and each model Y costs $150. l3e profits are: $30 for each X and $40 for each Y. The total number of machines must be less than 2500 per month. The company can spend no more than $330,000 on costs. How many of &ch should be produced to maximize the profit? m 1 dsbb < a s-0 0 '5-0 \3ao,o9o -- (Lo -? Find the indicated term of the sequence: b. Geometric: Page 616 (15-28) Find the 30~ term of the sequence 1 a. Arithmetic: Page G EG (9 - f 4) l> 5,9, 13, - -. = 64, b-k - - a, + (* -hd - * (fl-~\~ a d - Find the 1 2fi term of the sequence ai = -3-3,6,-12,24,... r=-z A,K-i

9 23. Write each series in sigma nolation. Page 609 ( l 1-16; (part A only); 55-58) a. Write in sigmanotation: a f3;~~+/~1,~,a,'c3~-1 c. P ~/-~.,.5- + ~ > Find the common difference or the common ratio. Page 616 (, 2) a. Find the common difference: b. Find the common ratio: The first term of an arithmetic sequence is -9 The first term of a geometric sequence is 2 2 and the tenth term is 15, Find the common and the fourth term is -. Find the d 125 common ratio. difference. &= a,+~n-[\,d 25. Sum of an Tnfinite Geometric Sequence: Page 61 7 (3 1,321 a. Find the sum, if it exists: b. Find the sum, if it exists: