&
Serie
Sequences

I

Series
st
time
cfw_
sequences
:
Definition :
infinite
an
n znt
series
Given
infinite series
an
5n=
Example
if
5h
if
Sn
converges
z
55
5h
subtract
It tz
=
tzsn
Yz
say
we
say
t
+
as
we
tgt
%
=
Yq
It Yzt
.
stg
+
.
.
.
of things ?
.
.
Polarcoordinalesl
Problem
Consider the
:
1) Find
the
between the
area
2) Find the
arc
8
curve
OEOE
for
r=O
spiral given by
x
AWAY
'T
axis
.
length
"
1)
A=f
trsndo
to "tso
2)
fifth
do
ted
=f"
'
do
t.to#=Tf=ftAdo
.
Frito
=
Et
=
Find
area
enclosed
inside
r=
Lecture
10.2

Calculus of
We looked at
Parametric
Curves
=
defined
curves
x=fH )
How do
we
by
for
y=gH)
and
do calculus with parametric
parameter t
curves
?
Man ent lines koncavity
under curves
2)
Aka
3)
Tangents
Find
length
are
& Concavity
Let
and
! be
Thecydoi
Definition
:
of radius
A circle
and trace out the
r
curve
is
rolling
that P
in
straight line
a
follows The
resulting
.
Fix
a
.
is
curve
point, p
,
the
cycloid
: .=
.
Parametric
.
.
.
.
.
.
.
.
Representation
:
0
r
Y

,
p
;[
a
x.

y=r
Why
ro


w
9.
I'i' .15., mm. #30. {HI/102, fgmf'burg 3:304:20, 353/133, "
[mmrms: "1111» «um «mm. a! 6 mm 1118 papa. Mata your '
swamaw plum Us: the bubo! m if you and
15y M madly I'm tho. who! my
' , (mi 31/ 3 / Math 1XX3 (5
\i A IN 1?}: n
x l I) ,e._._mw
Test # 3
Math 1XX3
March 27. 2015
T2=Thum 3:304:20. ESE/138, T3=Thum 4:305:20, HH/IOZ
TI=Man 9301020. HH/IO2.
Instructions: This exam consists of 6 questions in 9 pages. Indicate your answers clearly in the
appropriate places. Use the backs of pages i
Sequent
.
queries
A
sequence
is
A
Remark
:
list of
a
You
.az
,
to
as
cfw_n
1
at
.
as
,
Recursive Definition
:
'
.
.
prescribed order
a
.
as
function
a
new
integer
every
5

.
,
think of this
can
,=2
a
93
,
associate
Notation :
numbers in
10
'
a
'
+13nF
2