2006 Summer Semester
Problem Set III for Math 171
I. Find the following limits if they exist:
lim x2-1
tim x3-1
(a) X -.. 1XZ - ý
(b)
x -+ <x>X3 + 1
2. Find the compoundamountof an investmentof $4000for five yearsat the rateof
100/0
compoundedsemiannuaIlyo
(Give the equation;you do not needto estimate)
3. A deptof$IOOOdue in five yearsis to be repaidby a sinile paymeDtnow. Find
how muchthe paymentis if an interestrate of 8% compoundedquarterlyis assumed.
(Give the equation)
4. a) lim
- ~X - 7~lim 33-~x-7x3
t +:l
1-+2t + 2
1-+2
lim~
c) lim(t
I' ---~-2
lim(ý-1)3
- 1)3 d) lim
im
b)
b) lim..!!::.-lim~
-
.~-."
..,~2 -5x3
c_3
x-'-7+2x2
r_.2
r~r2
12
t +-4L
I-+-l
i~
1-
+1
-ý-1
I.
X-+-l
~
x-+-(4y-ý)3
~-(4x-ý)3
I.
-Sxx~ h) x-+u
S
X -t- X
ým
g) im 4 - X2
.r-+0-X + x2
5. If 1000is investedat an annualrateof3% compoundedcontinuously,find the
f) lim
1-2 1+2
.r-+-2+
compoundamountat the endof eight years.(Give the equation)
6. Find all points ofdiscontinuity for the function j(x)
E.=r;!X -x
7. Find the slopeof y= 5-6x-2x3whenx=2.
8. Find the equationof the tangentline to the curvey=
~
at the point (I ~5)
X
9. a) y= 2X2 +1
2
y ~=?
( 8x-t )3
c)y=
y'=?
2x+1
e) y = ýoox-3+ loV2X
y'=?
y = lOOx-3
b) -d-3
i=?
dx (3x1+ 1)3
d
d) _(5X2+2-Fx~)=?
dx
i
t) -(d Sx. -7tl i )
dx 2x+5
---h..-
dc
-.
dp
.~-
2008 Summer Semester
Problem Set III (or Math 171
I) Due to ineffectiveadvertisingIstek Vakfýfinds that its annualrevenueshavebeencut sharply.Moreover,the
revenue,r, at the end of t yearsof the businesssatisfiesthe equation r = 200,OOOe-o.2/. Find the annual revenue (r)
at the end of two yearsand at the endof dtreeyears.
2) Supposeattendingto a certaincollegecost $2i ,SOOin the 200(}.200i schoolyear.
This price includestuition , room, board,boocsand other expences.Assumingthe effective 6 % inflation, determine
what the collegecostswill be in the 20i (}.20i i schoolyear.(Give the equation)
3) Find the compoundamountof an investmentof $4000for five yearsat the rateof 10%compoundedsemiannually.
(Give the equation;you do not needto estimate)
4) A deptof$l000 due in five yearsis to be repaidby a singlepaymentnow. Find how much the paymentis if an
interestrate of 8% compoundedquarterlyis assumed.(Give the equation)
S) Find the effectiverateof interestif a nominalrateof 8% compounded
a)
annually.
b)
quarterly.
c)
continuously
6) If i 000 is investedat an annuaýrate of 3% compoundedcontinuously,find the compoundamountat the end of eight
years.(Give the equation)
7) Find the following limits if they exist:
tim x2-1
lim x3-1
(b)
X -.1 X2 -1
8. a)
lim 3-2x-7x3
~-'-7+2x2
X ~ co X3 + 1
b) lim~
-SX3
c) lim(t -1)3 ýd)}~
1-
,._,2 +1
2
(4x-l)~'"
. -~ b) lim 5 2
g) %-.-2
tim. 4 - X 2
%-.0-x + x
(1-4
t2 -4
t) LÝM
1-+-2(+ 2
e) ~~ 1+2
-
9)Computethe following limits
a)
Ilm
5of:2
Jf4.1
d)
-13
m2- 5
100
lim
z-+~
-~
b)
li
~
-
7M
m
JI-+O ~
Ilm
e)
~+5
.-+-~
c)
furýz-+2
.i:.:;.!
z-2
s+T
31;+5
10)
ifz 0(-1
if-loS z< ý
if.Z' = 1
if 1 < :z;S 2
if.Z' > 2 .
a.)
Jim j(.z)
1+
üm [(z)
d.) .~ý...
lim
b.) _-+-1-
j(z)
Jim j(z)
e.) ..-+1-
Iim 1(3:)
c.) _-+-ý
ý'
f.).~
J J). Find all poÝntsofdiscontinuity for the function I(x)
j(z)
= x-7
3
X -X
12). FÝndthe poÝntswhere f is discontÝnues a) [(X)
.
.
{ 2%-1 Ý}
ififx>l
x sýý'
2~ -1 Ý)
b) f(x) =
{
ifx>l
ex-I
eX
-I
ifxSl