MTH 111/CCE

University of Rhode Island

Instructor: Dr. M. Kulenovic

Exam #2

                                                                       Providence 4/03/98
Please show your work
1.   Show that x - 4 is the factor of the polynomial P(x) = x3 - x2 -10x - 8  and using that sketch the graph of this function.
 
2.   Find x- and y-intercepts and all the asymptotes of the function f(x) = (x2 + x - 2)/(2x2 - 9x + 9). Sketch the graph of
this function.

3.  Find all the asymptotes of the function f(x) = (x2 + 4)/(x - 1).

4.  Find the inverse function of the function  f(x) = 5x-1 + 4.  Sketch the graphs of  f and f -1 on the same coordinate axis.

5.   Solve for x:  (a)  4x+2 = 1/2                                    (b)  5x+1 = 7.

6.   Find the balance for $ 8,000 invested at rate 7% for 5 years, compounded
(a)  quarterly                                              (b)  continuously.

7.   Solve: log3 x + log3 (x + 2) = 1.

8.   Let log 2 = A, log 3 = B, log 7 = C. Express log 24/49 in terms of A, B and C.

9.  Express as a single logarithm:  ln (x2 - 9) + 2 ln (1/(x+3)) + 4 ln x  (x>3).

10.  You want to invest $ 10,000 for 5 years, and you have a choice between two accounts. The first pay 6% per year
compounded annually. The second pays 5% per year compounded continuously. Which is the better investment ? Justify
your answer.