The Most Important Problems to
Understand - This Week
7. Given the supply function
and the demand function D ( x ) is p  80e
1. Simplify the following expressions:
 3x 2 y 3

 x  yz

a.
b.
x
m
y m 1 




8. Change each of the following expressions to
logarithmic form.
103  0.001
2
b. 5  0.04
x 1
c. a  b
a.
2. Solve the following algebraically for x:
a.
b.
64
1
x 2
3
2
4x

4096
9. Given
x3 2 x  9 x  2 x  0
log a  2   m, log a  3  t , log a  5   h ,
evaluate: a.
log a  30  
b.
log a 1.5 
3. Determine the domain:
a.
ye
b.
ye
c.
y  ex
x 1
x2
5 x
.2 x
have units of dollars, and x is in hundreds of
items. Use your calculator to find the equilibrium
point. a. equilibrium price ______________
b. equilibrium quantity ___________
4
 m 1
S  x  is p  20e0.1x
10. Solve for x :
d.
y  eln x
x2
e. y  x 1
e
a.
ln  x  1  ln  x  2   2 ln  x 
b.
log  x   2 log  x  3  4
11. Find the limit of each of the following:
a. lim ( )
x 2
b. lim ( x  4 x)
2
4. How much will be in an account after 8 years on
a $1000 deposit in an account that earns a rate of
x 3
c. lim f( x) where
x2
1
4 % per year : a. compounded continuously.
2
 x  1, x  0

f ( x)   x 2  1, 0  x  2
4 x  1, x  2

b. compounded monthly.
c. compounded weekly.
5. What is the effective yield given an annual rate of
12% and the interest is compounded:
a. weekly
b. semiannually
c. continuously.
d. lim f( x)
x2
e. lim f( x)
x2
12. Evaluate
g ( x) 
ex 1
at each of the following
x
points:
6. Jim and Janet want their college savings account
for their daughter to be at $50, 000 in 18 years.
How much should they deposit now in an
account paying 5.25% per year
compounded continuously?
x
g(x)
1
.5
.1
-.01
0
DNE
.01
0.1
0.5
1
b. Estimate from the chart
lim g( x)
x 0
x4
13. lim
=
x4
x4
14.
lim
h 0
f 1  h   f 1
2
where f  x   x  x
h
x2  9
15. lim 2
x 3 x  7 x  12
16.
lim
h 0
5  h
2
 25
h
17. Determine the interval(s) over which f(x) is
continuous.
 x 1
x2, x  0

f ( x)   x 2  9, 0  x  5
2 x  6, x  5


© Marcia Drost
Sept 15, 2014