The document discusses the role of the Comptroller and Auditor General (CAG) of India and former CAG Vinod Rai. It provides background on the CAG, describing its responsibilities to audit government spending and report to Parliament. It then discusses Vinod Rai's tenure as CAG from 2008 to 2013, during which he exposed several major corruption scams through CAG reports, including the 2G spectrum scam, coal allocation scam, and Commonwealth Games scam. The document emphasizes Rai's role in strengthening the CAG's powers and pushing for reforms to bring more government activities and private-public partnerships under its audit purview.
This document provides information about countries and nationalities in French. It lists the names of several countries along with their gendered definite articles in French. It also explains that French nationalities change form depending on the gender and number of the person being described, with examples of how to transform masculine forms into feminine ones. The purpose is to teach some basic facts about expressing countries and nationalities in French.
This document discusses classroom-based evaluation and planning evaluation. It describes a four-step process for classroom-based evaluation: identifying purposes, collecting information, interpreting information, and decision making. Examples of decisions made in the classroom include changing purposes, plans, and practices based on student needs and characteristics. The document also provides a strategy for classroom-based evaluation involving comparing plans and objectives to student needs and assessing if objectives are being met. It suggests beginning evaluation before instruction and collecting student background information. Questions to consider when planning evaluation include who will use results, what will be assessed, and when assessment will occur.
HT Media Limited is an Indian media company with holdings in print, electronic, and digital media. It operates 19 printing facilities across India and several online businesses including Hindustantimes.com. A financial analysis of HT Media from 2010-2013 found that return on equity decreased 6% due to a 1% increase in net profit margin but 7% decrease in asset turnover. The main drivers for increased net profit margin over this period were decreased employee, selling, and interest costs.
The document discusses several regional dialects in the United States. It identifies the Southern dialect, originating from Africa and developed through slavery, as the most widely recognized. It is characterized by dropping "g" sounds and using words like "y'all" and "ain't." The New York/New Jersey dialect developed from British rule and Jewish immigration, dropping "t" sounds and using words like "coffee" and "soda." The Midland dialect formed the basis for standard English today, while the Western dialect emerged later as people migrated westward.
The document discusses the role of the Comptroller and Auditor General (CAG) of India and former CAG Vinod Rai. It provides background on the CAG, describing its responsibilities to audit government spending and report to Parliament. It then discusses Vinod Rai's tenure as CAG from 2008 to 2013, during which he exposed several major corruption scams through CAG reports, including the 2G spectrum scam, coal allocation scam, and Commonwealth Games scam. The document emphasizes Rai's role in strengthening the CAG's powers and pushing for reforms to bring more government activities and private-public partnerships under its audit purview.
This document provides information about countries and nationalities in French. It lists the names of several countries along with their gendered definite articles in French. It also explains that French nationalities change form depending on the gender and number of the person being described, with examples of how to transform masculine forms into feminine ones. The purpose is to teach some basic facts about expressing countries and nationalities in French.
This document discusses classroom-based evaluation and planning evaluation. It describes a four-step process for classroom-based evaluation: identifying purposes, collecting information, interpreting information, and decision making. Examples of decisions made in the classroom include changing purposes, plans, and practices based on student needs and characteristics. The document also provides a strategy for classroom-based evaluation involving comparing plans and objectives to student needs and assessing if objectives are being met. It suggests beginning evaluation before instruction and collecting student background information. Questions to consider when planning evaluation include who will use results, what will be assessed, and when assessment will occur.
HT Media Limited is an Indian media company with holdings in print, electronic, and digital media. It operates 19 printing facilities across India and several online businesses including Hindustantimes.com. A financial analysis of HT Media from 2010-2013 found that return on equity decreased 6% due to a 1% increase in net profit margin but 7% decrease in asset turnover. The main drivers for increased net profit margin over this period were decreased employee, selling, and interest costs.
The document discusses several regional dialects in the United States. It identifies the Southern dialect, originating from Africa and developed through slavery, as the most widely recognized. It is characterized by dropping "g" sounds and using words like "y'all" and "ain't." The New York/New Jersey dialect developed from British rule and Jewish immigration, dropping "t" sounds and using words like "coffee" and "soda." The Midland dialect formed the basis for standard English today, while the Western dialect emerged later as people migrated westward.
2. Cálculo Diferencial con “Mathematica”
:f →
2
2
1
; 0
1( )
; 0
2 1
x
x
xf x
ax b
x
x x
+
≤
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+
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% + % % (,
(-
% + % ' %. % +
(,
/ % % (, (-
( ,
0 0
lim ( ) lim ( ) (0)
x x
f x f x f+ −
→ →
∃ = =
1
1
1
1
lim)(lim
12
lim)(lim
2
00
200
−=
−=
−
+
=
=
++
+
=
−−
++
→→
→→
b
x
x
xf
b
xx
bax
xf
xx
xx
(- 0 - (, ! (-,
'
2
2
= '(2)= 0
2 1 x
ax b
f
x x =
+
=
+ +
20220)2('
)1(
2
)1(
22
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)1(2)()1(
12
13
334
2'
2
==−+=
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−−
=
=
+
−−+
=
+
/+/+−+
=
++
+
−=
/
/
aaaf
x
axba
x
baxaax
x
xbaxxa
xx
bax
b
$ (1)* (-
%+ % ' % % + (,
2 + (, % % % )0(')0(' −+
=∃ ff
3. Cálculo Diferencial con “Mathematica”
2
00
2
2 22 0 0
1
(0 ) (0) ( 1)
'(0 ) lim lim
2 1 ( 1) 4
lim lim 4
( 1) ( 1)
hh
a h h
b
ah b
b
f h f h
f
h h
h h h
h h h
+
+
→→
= → →
=
+
−
+ − +
= =
− + + +
= = =
+ +
2
0 0
2
0 0
1
1
(0 ) (0) 1'(0 ) lim lim
1 1 ( 1)
lim lim 1
( 1) ( 1)
h h
h h
h
f h f hf
h h
h h h h
h h h h
− −
−
−
→ →
→ →
+
+
+ − −= =
+ + − +
= = = −
− −
$ (1) (-.! 0,3
≠ 0,1
. % + (,
5. Cálculo Diferencial con “Mathematica”
22( ) '( ) 0 6 6*44 2*144 0 12(3 22 24) 0
max
V t a t t t t t= = − + = − + =
11 7
6
3
11 7 4
3 3
44 4.121 4.3.6.4 22 2 121 72 11 49
6 6 3
t
+
=
−
=
± − ± − ±
= = = =
( )
.min60)1236(12)6(
.max
3
4022
3
4
612
3
4
)226(12)(
VtV
VtV
ttV
=−=
=−=
−=
9@6 ()=) )87 /
= ( 196- /
4
3
3 6 8
t
1000
500
500
s t
V 3 0
V 8 0
a 4 3 0V 0 0
a 6 0
A % %
t (-∞,4/3) 4/3 (4/3,3) 3 (3,6) 6 (6,8) 8 (8,∞)
S(t) S 161 S Smax -1024 Smin S
SgnV + + + 0 - - - 0 +
V(t) V Vmax V V=0 V Vmin V 0 V
Sgn a + 0 - - - 0 + + +
6. Cálculo Diferencial con “Mathematica”
4 % % B % % % CD % % % %
.E ; 4 % .E( 8., ; % + (7
+ ,.7 @%. % ,.7 % (,
% ABO ˆ %
! #$
! % + OBA
x 8 x
v 0.5 t
y 5
A 8,00
B
OBA γ α β= = + *
tan tan
tan tan( )
1 tan *tan
α β
γ α β
α β
+
= + =
−
8
tan ; tan
5 5
x x
α β
−
= =
% ; % % ,.7
0,5 8 0,5
( ) arctg arctg
5 5
t t
tγ
−
= +
( )tγ % % ( ) 0tγ ′ =
7. Cálculo Diferencial con “Mathematica”
2 2
2 2
2 2 2 2
2 2 2 2
2 2 2 2
0,5 0,5
5 5( )
0,25 (8 0,5 )
1 1
5 5
2,5 2,5 10 10
25 0,25 25 (8 0,5 ) 100 100 (16 )
10(100 16 32 100 ) 10(16 32 )
(100 )(100 (16 ) ) (100 )(100 (16 ) )
t
t t
t t t t
t t t t
t t t t
γ ′ = − =
−
+ +
− = − =
+ + − + + −
+ − + − − −
=
+ + − + + −
2
2
2 2
10(16 32 )
( ) 0 0 16 32 0 8
(100 )(100 (16 ) )
t
t t t
t t
γ
−
′ = = − = =
+ + −
máximo.
% % % . (8.% $ (,.7 F 8( 9* 81 (9
8. Cálculo Diferencial con “Mathematica”
; % % -, G + %
E % ; % % % +
! + B % E ' % ;.
' + B E! !; . % % .%
+ % 8, G @' + % -, G @'
! #$
B
20 Kmd
A x
a
C
a - x
% !
E
H % )
20
)(20
20
22
1
xad
t
v
e
t
t
e
V
−+
==
==
H % -
80
2
x
t =
9. Cálculo Diferencial con “Mathematica”
:
8020
)(20 22
xxa
t +
−+
=
2 5
[ ]a0,x,
8020
)(20
)(
22
∈+
+−+
=
xxa
xt
% %$
% % + (, (
% % % 0 ( ,
2 2
4
2 2
1 2( ) 1
'( )
20 802 20 ( )
'( ) 0 80( ) 20 20 ( ) 0
a x
t x
a x
t x a x a x
− −
= +
+ −
= − − + − − =
2 2
2 2 2
2 2
4( ) 20 ( )
16( ) 20 ( )
15( ) 20
a x a x
a x a x
a x
− = + −
− = + −
− =
0
20 20
15 15
a x x a− = = −
∃ 0 ∀ ∈I,. J
% %
( ,.
2 2
1
20
20
a
t
+
=
( . 2 1
80
a
t = +
(
15
20
−a .
2 2
2
3
20 20
20
15 15
20 8
a
t
+ −
= + . %
10. Cálculo Diferencial con “Mathematica”
4% E ( -
H 9 E % B C B ,D ;(1- -
38
; % % % % % %
! #$
% % % % % ( ,.
%% %
B
A
A
( ) ( )
( ) ( )8,080
0,000
→=
→=
B
A
S
S
/ % % + % % %
B %
11. Cálculo Diferencial con “Mathematica”
t=4
t=0t=2
min
V 0
484)2(
02)(
2042)('4)( 2
−=−=
∀=
==−=→−=
A
A
AA
S
mínimottS
tttStttS
E 19., % (-
' + % . %
% + % + ,., % (9
B
( )
00)('
.04)(
00461)('88 2
∀
−=
==//−=→+−=
ttS
máxtS
tttSttS
B
B
BB
; % ,.8 % B
% ,., % (-
% % %
12. Cálculo Diferencial con “Mathematica”
SB
SA
22
)( BA SStd +=
( ) ( )2222
824)( +−+−= ttttd
F 4 % %
( ) ( )
( ) ( ) ( ) ( )
2 22 2
1
2 2
1
2 2
2
( ) 4 2 8
'( ) 2 4 * 2 4 2* 2 8 * 4
4 2 4 8 8 2 8
4 5 6 8
d t t t t
d t t t t t t
t t t t t t
t t t
= − + − +
= − − + − + −
= − − + − − +
= − −
1 2 2
4
5
0
'( ) 0 6 36 160 6 14
5 6 8 0
10 10
t
d t
t t t
−
=
= ± + ±
− − = = = =
A B
t=2 SA(2) = -4
t=2 SB(2) = 0
4 % % E ; 5 % ' % B
13. Cálculo Diferencial con “Mathematica”
' % % % % % 7G
E % E . % ;
% % = G E %
% % + -G @' 9 G @'
! #$
A
6 K m
B
5 K m
P
d
x 6 -x
1 2
2
25 6
;
2 4
d x c x
t t
V V
+ −
= = = =
5 % .
4
6
2
25
)(
2
xx
xt
−
+
+
=
% %$
% % + (, (=
% + %
4
1
252
)('
2
−
+
=
x
x
xt
14. Cálculo Diferencial con “Mathematica”
2 2 2 2
0
25 5
'( ) 0 2 25 0 25 4
3 5
t x x x x x x x= − + = + = = =
% %
( , 4)0( =t
( = 8,7
2
3625
)6( ≈
+
=t
,(
5
5
2
0
55
625
5 5( ) 3,68
2 4
t x
−+
= + = .
15. Cálculo Diferencial con “Mathematica”
K % % + % % % %
% . % %
! #
$
hrrrS ππ 22)( 2
+=
% + % % % $
2
2
r
V
hhrV
π
π ==
2
2
2
3
2
( ) 2 2
2
'( ) 4 0
2
4
2
v
S r r r
r
V
S r r
r
V V
r r
r
π π
π
π
π
= +
= − =
= =
16. Cálculo Diferencial con “Mathematica”
h
y
r
R
L + % % A
! #
!
( ) [ ]
R
8
2
r ==
=−
−
=−
=
/−
/
/+−+//=
∈⋅−=
−+=
⋅=
/
22
2
22
22
2
22
2
222
222
22
2
8
2
2
2
0
2
2
1
24)('
,02)(
2
)(
Rr
r
rR
rR
r
rR
rR
r
rrRrrV
RrrrRrV
rR
H
rhrV
ππ
π
π
!
/ ( )@6 %
[ ]
( )
( )
RrRrRRr
RRrrrRR
RrrRR
rrRrRR
rR
r
rRR
rR
r
rrRrrrV
RrrRRrrV
rRRyRh
3
22
9
8
04129
412494
232
22
2
0
2
2
3
1
3
2
)('
,0
3
1
)(
22222
4222222
2222
22222
22
2
22
22
222
222
22
===+−
+/=−//
−=−
=−+−
−
=−+
=
−
/−
/
/
+−+//
/
=
∈−+=
−+=+=
/
ππ
π
R
r
h
17. Cálculo Diferencial con “Mathematica”
L % % % % % %
. % % %
2 2
2
2 2
2
2
( ) 2
2
'( ) 2 0 0
2
2 0 máximo
2
P r
P r x x
P r
A r r r Pr r
P
A r r P r y x
P
A
π
π
π
π π
π
π
π
π
−
= + =
−
= + = −
= − + = = =
= −
x
r
18. Cálculo Diferencial con “Mathematica”
% + %
9@M +
( )
2
2
2
2
2
2
1
3
4
1
( ) 1
3
'( ) 2 1 2 0
2 4 1 4
0 x a ( ) Vcono
3 9 3 9
Volumen del cono a b
Volumen del cilindro x y
b b x
tg y a x b
a a x a a
x
V x x b
a
x b b x
V x xb x xb
a a a
x V x a b
π
π
ϑ
π
π
π π π
π
=
=
= = = − −
−
= −
/ /
/= − − = − =/
≠ = = ⋅ =
b
y
-a
x x
O
a