MTH 111/CCE

University of Rhode Island

Instructor: Dr. M. Kulenovic

Final Exam

                                                                       Providence 5/02/98
Please show your work
 
1.   Solve for x and write the solution set in the interval notation: |2x + 1| < 7.

2.   Find the domain of

3.   Find the standard equation of the circle which  center is at the point  (1,1) and which passes through the point (2,-1).

4.   Find the inverse of the function f(x) = (x + 2)/(2x - 5). What is domain of the inverse function?

5.   Find the equation of the line which goes through (-2,4) and is perpendicular to the line  2y - 8x + 4 = 0. Sketch the graph of this line.

6.   Identify the vertex, axis of symmetry, x-intercept(s), y-intercept, and the range for y = 2x2 - 7x - 4. Sketch the graph of this function.

7.   Find x- and y-intercepts and all the asymptotes of the function f(x) = (x2  - 4)/(3x2 + 11x - 4). Sketch the graph of
this function.

8.  Find the inverse function of the function  f(x) = 2x-1 - 4.  Sketch the graphs of  f and f -1 on the same coordinate axes.

9.   Find the balance for $ 10,000 invested at rate 6.5% for 8 years, compounded
(a)  quarterly                                              (b)  continuously.

10.   Solve: log2 x + log2 (x - 4) = log2 (x + 24) .

11.   Use calculator if necessary to solve for x:
(a)   4x 112x - 1 = 19  to four significant places.
(b)   log (x - 1) - log (x + 2) =1.

12.
(a)  Given that q is in quadrant II and  sin q = 2/5 find cos q .
(b)   Find the exact length of the arc intercepted by the central angle q = 240o  in a circle of diameter 10 feet.

13.   Let  f(x) = 2 cos(2x - p/2 ). For this function find its amplitude, period, and phase shift and sketch its graph on the interval [0,2p].

14.  The angle of elevation of the top of a hill from point A on the ground is 25o . From the point B, 70 feet closer to the hill,  the angle of elevation is 30o .
(a)  What is the height of the hill ?
(b)  What is the distance from the base of the hill to the point A ?

15.   Find the exact value of cos (.a - b ), given that sin a = 2/7, and  be an angle in quadrant I and  cos  b =-1/4, and b be an angle in quadrant II.

16.   Find the exact values of  sin (2q), and cos (q/2)  given  sin q = 5/13, and  q be an angle in quadrant I.

17.   Find the angle between the lines   y = x + 4, and  y = -2 x + 1.

18.   Find all solutions to  cos2 x = 1/4 in the interval  (0,2p).

19.   Solve the triangle for which a = 10, b = 40o , and  g = 60o . Find the area of this triangle.

20.  A surveyor found that two sides of a triangular lot were 210 ft, and 188 ft, with an included angle of  75o . Find the length of third side and the area of this lot.