KJ Somaiyya Medical College & Research Centre, Mumbai
algebra
MATH 123

Spring 2013
MATH 2060 Mathematical Analysis II
midterm suggested solution
Lee Man Chun
Q1 Let f be a Riemann integrable function defined on [a, b].
(a) Show that the square function f 2 is also integrable function on [a, b].
Proof. Since f R[a, b] , there exists M >
KJ Somaiyya Medical College & Research Centre, Mumbai
algebra
MATH 123

Spring 2016
Table of Contents
The MetaTrader 4 Platform
Main Menu Window
Market Watch Window
How to Work With Candlesticks
How to Change Colors
How to Change Chart Period
How to Open/Close Positions
How to Add Stop Loss/Take Profit
How to Execute Pending Orders
Platf
KJ Somaiyya Medical College & Research Centre, Mumbai
algebra
MATH 123

Spring 2016
Table of Contents
Momentum
Stochastics
Relative Strength Index (RSI)
MACD
o
Crossovers
o
Divergence
o
Dramatic Rise
Momentum
Momentum is a general term used to describe the speed at which prices move over given time
periods.
Momentum indicators determine
KJ Somaiyya Medical College & Research Centre, Mumbai
algebra
MATH 123

Spring 2016
[PDF] Book Obs And Gynae Mcqs.PDF [BOOK]
Obs And Gynae Mcqs
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KJ Somaiyya Medical College & Research Centre, Mumbai
algebra
MATH 123

Spring 2016
Table of Contents
Introduction to Technical Analysis
Recognizing Trends
Equidistant Channels
Moving Averages
Support and Resistance
Bollinger Bands
Parabolic SAR
Introduction to Technical Analysis
There are many different methods and tools utilized in tec
KJ Somaiyya Medical College & Research Centre, Mumbai
algebra
MATH 123

Spring 2016
Meta Trade 4 Mobile application, MetaQuotes Corp.
Please follow these instructions to install the Meta trader mobile trader onto your iPhone
3G/3GS/4, iPod Touch and iPad with iOS 4.0 and higher.
This is a onetime process.
1. Enter the App. Store and sea
KJ Somaiyya Medical College & Research Centre, Mumbai
algebra
MATH 123

Spring 2016
Learn How to Trade Forex
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KJ Somaiyya Medical College & Research Centre, Mumbai
algebra
MATH 123

Spring 2013
Suggested solution of HW7
P.270 Q7: (a)
P
an is absolutely convergent and bn is bounded. Then there exists M > 0 such
that
bn  M
n N.
for all
And there exists C > 0 such that for all p N, we have
p
X
an  C.
n=1
Thus, for any p N,
p
X
an bn  M
n=1
p
KJ Somaiyya Medical College & Research Centre, Mumbai
algebra
MATH 123

Spring 2013
Suggested solution of HW7
P286, 1 a:
X
fn =
X
x2
1
, x R. For any x R, we have
+ n2
0
x2
1
1
2 , n N.
2
+n
n
P
Thus, by Weierstrass Mtest,
fn is uniformly convergent on R.
X
X
x
P286, 1 c:
fn =
sin 2 , x R. Since we have for all x R,
n
0  sin(
x
x
) 
KJ Somaiyya Medical College & Research Centre, Mumbai
algebra
MATH 123

Spring 2013
MATH 2060 Mathematical Analysis II
HW5 suggested solution
Lee Man Chun
P.246 Q4:
when x [0, 1) ,
0
n
when x = 1,
lim x = 1
n
+ when x > 1.
Thus,
0
n
x
1
lim
=
n 1 + xn
2
1
P.247 Q14:
Denote fn (x) =
when x [0, 1) ,
when x = 1,
when x > 1.
xn
and
1 + xn
0
KJ Somaiyya Medical College & Research Centre, Mumbai
algebra
MATH 123

Spring 2013
Suggested solution of HW6
P.252 Q6:
1
for x [0, 1].
(1 + x)n
If x = 0, then fn (0) = 1 for all n N. Thus limn fn (0) 1.
fn (x) =
If x (0, 1],
1
1+x
< 1. Thus fn (x) 0 as n . So we obtain the pointwise limit
function f : [0, 1] R at which
1
f (x) =
0
if x
KJ Somaiyya Medical College & Research Centre, Mumbai
algebra
MATH 123

Spring 2013
Suggested solution of HW4
P.215 Q17:
f is continuous function on [a, b]. Since f (x) > 0 on [a, b], by maxmin theorem, there
exists m = infcfw_f (x) : x [a, b] and M = supcfw_f (x) : x [a, b] such that
m f (x) M
x [a, b].
So, we have
b
Z
Z
b
g.
a
a
a
b
Z
KJ Somaiyya Medical College & Research Centre, Mumbai
algebra
MATH 123

Spring 2013
Suggested solution of HW3
P.215 Q2:
Let P : 0 = x0 < x1 < . < xn = 1 be a partition on [0, 1]. On each interval [xi , xi+1 ],
since Q is dense in R, Mi = xi+1 + 1 > 1 and mi = 0.
So, we have
U (f, P ) =
n
X
n
X
Mi xi >
i=1
L(f, P ) =
n
X
xi = 1.
i=1
mi xi
KJ Somaiyya Medical College & Research Centre, Mumbai
algebra
MATH 123

Spring 2013
Suggested solution of HW1
P.171 Q4:
Define : R R by
x
(x) =
0
if x Q
if x Qc .
Then f (x) f (0) = (x)(x 0) , for all x R.
Since (x) x, by squeeze theorem, (x) is continuous at x = 0. By Carath
eodorys
Theorem, f is differentiable at x = 0 and f 0 (0)
KJ Somaiyya Medical College & Research Centre, Mumbai
algebra
MATH 123

Spring 2013
Suggested solution of HW2
P.180 Q19:
Let > 0 be given, there exists > 0 such that if 0 < x y < and x, y I = [a, b],
then
f (x) f (y)
0
f (x) < /2.
xy
Interchange x and y, we obtain
f (x) f (y)
0
f (y) < /2.
xy
So if 0 < x y < and x, y I = [a, b]
KJ Somaiyya Medical College & Research Centre, Mumbai
algebra
MATH 123

Spring 2016
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KJ Somaiyya Medical College & Research Centre, Mumbai
algebra
MATH 123

Spring 2016
ROI The Miami Debate
Measurement and evaluation of communications is an enduring discussion in public
relations research and practice. Recently, there has been a move to adopt business and
management concepts and language in order to demonstrate the outco
KJ Somaiyya Medical College & Research Centre, Mumbai
algebra
MATH 123

Spring 2016
NeoVictorian Art and Aestheticism, University of Hull, 26 March 2011
BIOGRAPHICAL NOTES
Nadine Christina Boehm holds a PhD from the FriedrichAlexanderUniversity at ErlangenNuremberg, where she works as a lecturer in English literature and cultural stud
KJ Somaiyya Medical College & Research Centre, Mumbai
algebra
MATH 123

Spring 2016
FACTOTUM
Charles Bukowski
1
2
For John & Barbara Martin
The novelist does not long to see the lion eat grass. He realizes that one and the same God created the
wolf and the lamb, then smiled, "seeing that his work was good."
 Andre Gide
3
FACTOTUM
*1*
I
KJ Somaiyya Medical College & Research Centre, Mumbai
algebra
MATH 123

Spring 2016
1
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TABLE OF CONTENTS
TABLE OF CONTENTS . 4
INTRODUCTION. 5
CHAPTER 1 CHART ANALYSIS IN CURRENCY TRADING . 6
1.1  IMPORTANCE OF CHART ANA