MATH 203 Final, Spring 2008

(60%) Part I; Circle the correct answer on the table provided on page one (Multiple choices, with 2 points for cach corrcet answer and -0.25 point penalty on each wrong answer) 1. The two solutions of the quadratic equation 2x*-6x =0 are: -a) 3 and 0 b) 2 and 0 c) -3 and 0 2. ‘The solution of the logarithmic equation In ( 3x-5 )= b) (-29,-3) U (2,72) Cc) (-00,-2) (3,400) d) [2,+90) 5 , . Let y=f(x)=ix-S and g(x)= = then ffo(4)) = 2 Vx 10. log, 1+ log, 6-log, 3= a) log, 3 b) log, t b) 0 c) d) > . 5x-1 12. lim, _,9 re) 1 a)— 5 ™ and f(x)=x?-1 then g(0)-2/0) = a)2 b) 1 c) 0 d) 1 14. Consider the system { then the unique solution is: ~x+3y=-4 a) (1-1) b) (2-1) c) LI) d) (2,1) vx? -3x 15. The domain of definition of (x) = ——— is a x+l ajx¥-l, x#1 b) -35x<3 c) x£0,x23 16. The system 4x+y~=~-6 has xt+2y=5 \ a) no solution b) a unique solution initely many solutions d) exactly two solutions 20. Given f(x) J Hex<T en tim fQ) . (aiven x)= e. im a)- Y 2x41 if x21 rT J a)2 b) 4 c)3 dj. 1 24. If fx) =x? -1, then fZat])= c) 4a7(a+1) d) 4a(a+1) 24, The value of a truck is estimated by the function: V = f(t) = 45,000 -3,000¢ where V equals the value stated in dollars and t equals the age of the truck expressed in years, then the value of the truck will be equal to zero after: a)15 years c) 22 years d)12 years ays . A step of (3x3) Gaussian elimination method has produced the following arr: f Ip) 10 00 , then the solution set is: (0 1 -2 |0) a,x), )/x, =a, Hay =O} ~ 27.Domain f= aR 28.Range f- a) (3,:20) 29.The equation of the asymptote is: 3600q-45000 30. The profit function for a firm is: P (q) = -10q Where q equals the number of units sold and P equals annual profit in dollars. If 150 units were sold then the profit expected is equal to: a) $ 207 000 b) $ 249 000 c) $ 239 000 d) $ 270 000 4 (40%)Part LI (Answer each of the following questions in the space provided. Justify and show your work) 0 -7 |-20) 1) Given|0 -2 -12 | 18 0 0 5 {is} and determine the solution (x,,*,,;) , complete the remaining steps of the Gaussian method (8%) +2 if xs0 2* ifx>0 ™ 2) Sketch function f(x) =] b 3) Solve the following equations: a) x’?Inx-9Inx-0 c) |2x+3/-x-4 4) For cach of the following Gud the limit (if it exists): . x-3 a hm,_, = ae xt] (2%) ifx<1 ,x#0 Is f(x) continuous at x = 1? Justify your answer. 5) For cach of the following functions determine the derivative of y = f(x) using the tules of differentiation. (Don’t simplify your answer):