Download Review for Test 1 - University of Arizona Math

Review for Test 1
1. Simplify completely:
a. log 2 (log 2 4
2)
ln A 2  ln B 2  2
e
ln
 2 ln A
AB
a
c. tan(arccos )
b
x

d. sin  2 arccos 
2

b. 100
log A

2. Find the inverse function for
f ( x)  a  b ln( cx  d ) . What is the
domain of the given function? Find the asymptotes of this function and its
inverse.
3. The number of bacteria in milk grows at a rate of 10% per day once the milk
has been bottled. When milk is put in the bottles, it has on average bacteria
count of 500 million per bottle (initial value of bacteria).
a. Write an equation for f (t ) , the number of bacteria t days after the
milk is bottled.
b. Suppose milk cannot be safely consumed if the bacteria count is
greater than 3 billion per bottle. How many days will milk be safe to
drink once it has been bottled?
4. The distance from the particle to the certain point on the plane is given by
d (t )  at 2  bt
formula:
, where t is time in seconds and d is distance in
inches. Answer the following questions:
a. What is the initial distance?
b. At what time is the distance equal to Zero?
c. Given a  0 , what could you assume about a and b?
d. At what time is the distance the greatest? What would you say about a
and b?What is the value of the distance at this moment?
3x 3
continuous over the interval [1, 10]? Find all
x2  4
asymptotes of the graph of f(x).
5. Is the function f ( x ) 
6. Find the value of c that would make the function continuous. Explain.
 x 3  27
x  3

f ( x)   x  3
c
x  3

b  x for x  1
7. Given f ( x )  
, find value(s) of b that make f ( x )
2
 x  1 for x  1
continuous.
8. Find an equation of the trig. function given by the graph. Find period,
amplitude, etc.
9. For f ( x) 
x2
, find
x 2
lim f ( x)
x 
lim f ( x )
x2
lim f ( x)
x 2
lim f ( x)
x 
lim f ( x)
x 2
10. Derivatives (algebraically and numerically), equation of the tangent line,
graphs, etc.