#
MTH 111/CCE

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University of Rhode Island

Instructor: Dr. M. Kulenovic
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Exam #2

Providence 4/03/98
**Please show your work**
**1. **Show that x -
4 is the factor of the polynomial P(x)
= x^{3} - x^{2} -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)
= (x^{2} + x - 2)/(2x^{2} - 9x + 9). Sketch
the graph of

this function.
**3. **Find all the asymptotes of the
function f(x) = (x^{2} + 4)/(x - 1).

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

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

**6. **Find the balance for $
8,000 invested at rate 7%
for 5 years,
compounded

**(a) **quarterly
**(b) **continuously.

**7. **Solve:
log_{3}** **x + log_{3}**
**(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 (x^{2} - 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.