1. The document is about trigonometric limits and contains 7 pages with 34 solved limits. It uses fundamental limit laws and techniques like factorizing and applying trigonometric identities to find the limits.
2. Some of the limits involve factors like sinx/x, tanx/x, secx/x as x approaches 0 and techniques are shown to deal with indeterminate forms like 0/0.
3. The solutions find limits of combinations of trigonometric functions like sinx, cosx, tanx as the input x approaches values like 0, π/4, a using standard trigonometric limits and properties of limits.
Trigonometry 10th edition larson solutions manual.
Full download: https://goo.gl/gFVG5A
Peope also search:
algebra and trigonometry ron larson 9th edition pdf
trigonometry larson 9th edition pdf
algebra and trigonometry ron larson pdf
ron larson trigonometry 9th edition pdf
trigonometry 10th edition solutions pdf
algebra & trigonometry
algebra and trigonometry 10th edition pdf
algebra and trigonometry 10th edition free
KuberTENes Birthday Bash Guadalajara - K8sGPT first impressionsVictor Morales
K8sGPT is a tool that analyzes and diagnoses Kubernetes clusters. This presentation was used to share the requirements and dependencies to deploy K8sGPT in a local environment.
Low power architecture of logic gates using adiabatic techniquesnooriasukmaningtyas
The growing significance of portable systems to limit power consumption in ultra-large-scale-integration chips of very high density, has recently led to rapid and inventive progresses in low-power design. The most effective technique is adiabatic logic circuit design in energy-efficient hardware. This paper presents two adiabatic approaches for the design of low power circuits, modified positive feedback adiabatic logic (modified PFAL) and the other is direct current diode based positive feedback adiabatic logic (DC-DB PFAL). Logic gates are the preliminary components in any digital circuit design. By improving the performance of basic gates, one can improvise the whole system performance. In this paper proposed circuit design of the low power architecture of OR/NOR, AND/NAND, and XOR/XNOR gates are presented using the said approaches and their results are analyzed for powerdissipation, delay, power-delay-product and rise time and compared with the other adiabatic techniques along with the conventional complementary metal oxide semiconductor (CMOS) designs reported in the literature. It has been found that the designs with DC-DB PFAL technique outperform with the percentage improvement of 65% for NOR gate and 7% for NAND gate and 34% for XNOR gate over the modified PFAL techniques at 10 MHz respectively.
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
Online aptitude test management system project report.pdfKamal Acharya
The purpose of on-line aptitude test system is to take online test in an efficient manner and no time wasting for checking the paper. The main objective of on-line aptitude test system is to efficiently evaluate the candidate thoroughly through a fully automated system that not only saves lot of time but also gives fast results. For students they give papers according to their convenience and time and there is no need of using extra thing like paper, pen etc. This can be used in educational institutions as well as in corporate world. Can be used anywhere any time as it is a web based application (user Location doesn’t matter). No restriction that examiner has to be present when the candidate takes the test.
Every time when lecturers/professors need to conduct examinations they have to sit down think about the questions and then create a whole new set of questions for each and every exam. In some cases the professor may want to give an open book online exam that is the student can take the exam any time anywhere, but the student might have to answer the questions in a limited time period. The professor may want to change the sequence of questions for every student. The problem that a student has is whenever a date for the exam is declared the student has to take it and there is no way he can take it at some other time. This project will create an interface for the examiner to create and store questions in a repository. It will also create an interface for the student to take examinations at his convenience and the questions and/or exams may be timed. Thereby creating an application which can be used by examiners and examinee’s simultaneously.
Examination System is very useful for Teachers/Professors. As in the teaching profession, you are responsible for writing question papers. In the conventional method, you write the question paper on paper, keep question papers separate from answers and all this information you have to keep in a locker to avoid unauthorized access. Using the Examination System you can create a question paper and everything will be written to a single exam file in encrypted format. You can set the General and Administrator password to avoid unauthorized access to your question paper. Every time you start the examination, the program shuffles all the questions and selects them randomly from the database, which reduces the chances of memorizing the questions.
A review on techniques and modelling methodologies used for checking electrom...nooriasukmaningtyas
The proper function of the integrated circuit (IC) in an inhibiting electromagnetic environment has always been a serious concern throughout the decades of revolution in the world of electronics, from disjunct devices to today’s integrated circuit technology, where billions of transistors are combined on a single chip. The automotive industry and smart vehicles in particular, are confronting design issues such as being prone to electromagnetic interference (EMI). Electronic control devices calculate incorrect outputs because of EMI and sensors give misleading values which can prove fatal in case of automotives. In this paper, the authors have non exhaustively tried to review research work concerned with the investigation of EMI in ICs and prediction of this EMI using various modelling methodologies and measurement setups.
1. Limites Trigonométricos Resolvidos
Sete páginas e 34 limites resolvidos
1
Usar o limite fundamental e alguns artifícios : 1lim
0
=
→ x
senx
x
1.
x
x
x sen
lim
0→
= ? à
x
x
x sen
lim
0→
=
0
0
, é uma indeterminação.
x
x
x sen
lim
0→
=
x
xx sen
1
lim
0→
=
x
x
x
sen
lim
1
0→
= 1 logo
x
x
x sen
lim
0→
= 1
2.
x
x
x
4sen
lim
0→
= ? à
x
x
x
4sen
lim
0→
=
0
0
à
x
x
x 4
4sen
.4lim
0→
= 4.
y
y
y
sen
lim
0→
=4.1= 4 logo
x
x
x
4sen
lim
0→
=4
3.
x
x
x 2
5sen
lim
0→
= ? à =
→ x
x
x 5
5sen
.
2
5
lim
0
=
→ y
y
y
sen
.
2
5
lim
0 2
5
logo
x
x
x 2
5sen
lim
0→
=
2
5
4.
nx
mx
x
sen
lim
0→
= ? à
nx
mx
x
sen
lim
0→
=
mx
mx
n
m
x
sen
.lim
0→
=
n
m
.
y
y
y
sen
lim
0→
=
n
m
.1=
n
m
logo
nx
mx
x
sen
lim
0→
=
n
m
5.
x
x
x 2sen
3sen
lim
0→
= ? à
x
x
x 2sen
3sen
lim
0→
= =
→
x
x
x
x
x 2sen
3sen
lim
0
=
→
x
x
x
x
x
2
2sen
.2
3
3sen
.3
lim
0
.
2
3
2
2sen
lim
3
3sen
lim
0
0
=
→
→
x
x
x
x
x
x
. 1.
2
3
sen
lim
sen
lim
0
0
=
→
→
t
t
y
y
t
y
=
2
3
logo
x
x
x 2sen
3sen
lim
0→
=
2
3
6.
sennx
senmx
x 0
lim
→
= ? à
nx
mx
x sen
sen
lim
0→
=
x
nx
x
mx
x sen
sen
lim
0→
=
nx
nx
n
mx
mx
m
x sen
.
sen
.
lim
0→
=
nx
nx
mx
mx
n
m
x sen
sen
.lim
0→
=
n
m
Logo
sennx
senmx
x 0
lim
→
=
n
m
7. =
→ x
tgx
x 0
lim ? à =
→ x
tgx
x 0
lim
0
0
à =
→ x
tgx
x 0
lim =
→ x
x
x
x
cos
sen
lim
0
=
→ xx
x
x
1
.
cos
sen
lim
0
xx
x
x cos
1
.
sen
lim
0→
=
xx
x
xx cos
1
lim.
sen
lim
00 →→
= 1 Logo =
→ x
tgx
x 0
lim 1
8.
( )
1
1
lim 2
2
1 −
−
→ a
atg
a
= ? à
( )
1
1
lim 2
2
1 −
−
→ a
atg
a
=
0
0
àFazendo
→
→
−=
0
1
,12
t
x
at à
( )
t
ttg
t 0
lim
→
=1
logo
( )
1
1
lim 2
2
1 −
−
→ a
atg
a
=1
2. Limites Trigonométricos Resolvidos
Sete páginas e 34 limites resolvidos
2
9.
xx
xx
x 2sen
3sen
lim
0 +
−
→
= ? à
xx
xx
x 2sen
3sen
lim
0 +
−
→
=
0
0
à ( )
xx
xx
xf
2sen
3sen
+
−
= =
+
−
x
x
x
x
x
x
5sen
1.
3sen
1.
=
+
−
x
x
x
x
x
x
.5
5sen
.51.
.3
3sen
.31.
=
x
x
x
x
.5
5sen
.51
.3
3sen
.31
+
−
à
0
lim
→x
x
x
x
x
.5
5sen
.51
.3
3sen
.31
+
−
=
51
31
+
−
=
6
2−
=
3
1
− logo
xx
xx
x 2sen
3sen
lim
0 +
−
→
=
3
1
−
10. 30
sen
lim
x
xtgx
x
−
→
= ? à 30
sen
lim
x
xtgx
x
−
→
=
xx
x
xx
x
x cos1
1
.
sen
.
cos
1
.
sen
lim 2
2
0 +→
=
2
1
( ) 3
sen
x
xtgx
xf
−
= = 3
sen
cos
sen
x
x
x
x
−
= 3
cos
cos.sensen
x
x
xxx −
=
( )
xx
xx
cos.
cos1.sen
3
−
=
x
x
xx
x
cos
cos1
.
1
.
sen
2
−
=
x
x
x
x
xx
x
cos1
cos1
.
cos
cos1
.
1
.
sen
2 +
+−
=
xx
x
xx
x
cos1
1
.
cos1
.
cos
1
.
sen
2
2
+
−
=
xx
x
xx
x
cos1
1
.
sen
.
cos
1
.
sen
2
2
+
Logo 30
sen
lim
x
xtgx
x
−
→
=
2
1
11. 30
sen11
lim
x
xtgx
x
+−+
→
=? à
xtgxx
xtgx
x sen11
1
.
sen
lim 30 +++
−
→
=
xtgxxx
x
xx
x
x sen11
1
.
cos1
1
.
sen
.
cos
1
.
sen
lim 2
2
0 ++++→
=
2
1
.
2
1
.
1
1
.
1
1
.1 =
4
1
( ) 3
11
x
senxtgx
xf
+−+
= =
xtgxx
xtgx
sen11
1
.
sen11
3
+++
−−+
=
xtgxx
xtgx
sen11
1
.
sen
3
+++
−
30
sen11
lim
x
xtgx
x
+−+
→
=
4
1
12.
ax
ax
ax −
−
→
sensen
lim = ? à
ax
ax
ax −
−
→
sensen
lim =
−
+
−
→
2
.2
2
cos.
2
sen2
lim
ax
axax
ax
=
1
2
cos.
.
2
.2
)
2
sen(2
lim
+
−
−
→
ax
ax
ax
ax
= acos Logo
ax
ax
ax −
−
→
sensen
lim = cosa
3. Limites Trigonométricos Resolvidos
Sete páginas e 34 limites resolvidos
3
13.
( )
a
xax
a
sensen
lim
0
−+
→
= ? à
( )
a
xax
a
sensen
lim
0
−+
→
=
1
2
cos.
.
2
.2
2
sen2
lim
++
−
−+
→
xax
ax
xax
aa
=
1
2
2
cos.
.
2
.2
2
sen2
lim
+
→
ax
a
a
aa
= xcos Logo
( )
a
xax
a
sensen
lim
0
−+
→
=cosx
14.
( )
a
xax
a
coscos
lim
0
−+
→
= ? à
( )
a
xax
a
coscos
lim
0
−+
→
=
a
xaxxax
a
−−
++
−
→
2
sen.
2
sen2
lim
0
=
−
−
+
−
→
2
.2
2
sen.
2
2
sen.2
lim
0 a
aax
a
=
−
−
+
−
→
2
2
sen
.
2
2
senlim
0 a
a
ax
a
= xsen− Logo
( )
a
xax
a
coscos
lim
0
−+
→
=-senx
15.
ax
ax
ax −
−
→
secsec
lim = ? à
ax
ax
ax −
−
→
secsec
lim =
ax
ax
ax −
−
→
cos
1
cos
1
lim =
ax
ax
xa
ax −
−
→
cos.cos
coscos
lim =
( ) axax
xa
ax cos.cos.
coscos
lim
−
−
→
=
( ) axax
xaxa
ax cos.cos.
2
sen.
2
sen.2
lim
−
−
+
−
→
=
axxa
xaxa
ax cos.cos
1
.
2
.2
2
sen
.
1
2
sen.2
lim
−
−
−
+
−
→
=
axxa
xaxa
ax cos.cos
1
.
2
2
sen
.
1
2
sen
lim
−
−
+
→
=
aa
a
cos.cos
1
.1.
1
sen
=
aa
a
cos
1
.
cos
sen
= atga sec. Logo
ax
ax
ax −
−
→
secsec
lim = atga sec.
16.
x
x
x sec1
lim
2
0 −→
= ? à
x
x
x sec1
lim
2
0 −→
=
( )xxx
xx
cos1
1
.
cos
1
.
sen
1
lim
2
20
+
−
→
= 2−
( )
x
x
xf
cos
1
1
2
−
= =
x
x
x
cos
1cos
2
−
=
( )x
xx
cos1.1
cos.2
−−
=
( ) ( )
( )x
x
xx
x
cos1
cos1
.
cos
1
.
cos1
1
2 +
+−
−
=
( )xxx
x
cos1
1
.
cos
1
.
cos1
1
2
2
+
−
−
=
( )xxx
x
cos1
1
.
cos
1
.
sen
1
2
2
+
−
4. Limites Trigonométricos Resolvidos
Sete páginas e 34 limites resolvidos
4
17.
tgx
gx
x −
−
→ 1
cot1
lim
4
π
= ? à
tgx
gx
x −
−
→ 1
cot1
lim
4
π
=
tgx
tgx
x −
−
→ 1
1
1
lim
4
π
=
tgx
tgx
tgx
x −
−
→ 1
1
lim
4
π
=
tgx
tgx
tgx
x −
−−
→ 1
)1.(1
lim
4
π
=
tgxx
1
lim
4
−
→
π
= 1− Logo
tgx
gx
x −
−
→ 1
cot1
lim
4
π
= -1
18.
x
x
x 2
3
0 sen
cos1
lim
−
→
= ? à
x
x
x 2
3
0 sen
cos1
lim
−
→
=
( )( )
x
xxx
x 2
2
0 cos1
coscos1.cos1
lim
−
++−
→
=
( )( )
( )( )xx
xxx
x cos1.cos1
coscos1.cos1
lim
2
0 +−
++−
→
=
x
xx
x cos1
coscos1
lim
2
0 +
++
→
=
2
3
Logo
x
x
x 2
3
0 sen
cos1
lim
−
→
=
2
3
19.
x
x
x cos.21
3sen
lim
3
−→
π
= ? à
x
x
x cos.21
3sen
lim
3
−→
π
=
( )
1
cos.21.sen
lim
3
xx
x
+
−
→
π
= 3−
( )
x
x
xf
cos.21
3sen
−
= =
( )
x
xx
cos.21
2sen
−
+
=
x
xxxx
cos.21
cos.2sen2cos.sen
−
+
=
( )
x
xxxxx
cos.21
cos.cos.sen.21cos2.sen 2
−
+−
=
( )[ ]
x
xxx
cos.21
cos21cos2.sen 22
−
+−
=
[ ]
x
xx
cos.21
1cos4.sen 2
−
−
=
( )( )
x
coxcoxx
cos.21
.21..21.sen
−
+−
− =
( )
1
cos.21.sen xx +
−
20.
tgx
xx
x −
−
→ 1
cossen
lim
4
π
= ? à
tgx
xx
x −
−
→ 1
cossen
lim
4
π
= ( )x
x
coslim
4
−
→π
=
2
2
−
( )
tgx
xx
xf
−
−
=
1
cossen
=
x
x
xx
cos
sen
1
cossen
−
−
=
x
x
xx
cos
sen
1
cossen
−
−
=
x
xx
xx
cos
sencos
cossen
−
−
=
( )
x
xx
xx
cos
cossen.1
cossen
−−
−
=
xx
xxx
sencos
cos
.
1
cossen
−
−
− = xcos−
21. ( ) )sec(cos.3lim
3
xx
x
π−
→
= ? à ( ) )sec(cos.3lim
3
xx
x
π−
→
= ∞.0
( ) ( ) )sec(cos.3 xxxf π−= =( )
( )x
x
πsen
1
.3 − =
( )x
x
ππ −
−
sen
3
=
( )x
x
ππ −
−
3sen
3
=
( )
( )x
x
−
−
3.
3sen.
1
π
πππ
=
( )
( )x
x
ππ
πππ
−
−
3
3sen.
1
à ( ) )sec(cos.3lim
3
xx
x
π−
→
=
( )
( )x
xx
ππ
πππ
−
−→
3
3sen.
1
lim
3
=
π
1
22. )
1
sen(.lim
x
x
x→∝
= ? à )
1
sen(.lim
x
x
x→∝
= 0.∞
x
x
x 1
1
sen
lim
→∝
= 1
sen
lim
0
=
→ t
t
t
à Fazendo
→
+∞→
=
0
1
t
x
x
t
5. Limites Trigonométricos Resolvidos
Sete páginas e 34 limites resolvidos
5
23.
1sen.3sen.2
1sensen.2
lim 2
2
6 +−
−+
→ xx
xx
x π
= ? à
1sen.3sen.2
1sensen.2
lim 2
2
6 +−
−+
→ xx
xx
x π
=
x
x
x sen1
sen1
lim
6
+−
+
→π
=
6
sen1
6
sen1
π
π
+−
+
=
2
1
1
2
1
1
+−
+
= 3− à ( )
1sen.3sen.2
1sensen.2
2
2
+−
−+
=
xx
xx
xf =
( )
( )1sen.
2
1
sen
1sen.
2
1
sen
−
−
+
−
xx
xx
=
( )
( )1sen
1sen
−
+
x
x
=
x
x
sen1
sen1
+−
+
24. ( )
−
→ 2
.1lim
1
x
tgx
x
π
= ? à ( )
−
→ 2
.1lim
1
x
tgx
x
π
= ∞.0 à ( ) ( )
−=
2
.1
x
tgxxf
π
=
( )
−−
22
cot.1
x
gx
ππ
=
( )
−
−
22
1
x
tg
x
ππ
=
( )
−
−
22
2
.1.
2
x
tg
x
ππ
π
π
=
( )x
x
tg
−
−
1.
2
22
2
π
ππ
π =
−
−
22
22
2
x
x
tg
ππ
ππ
π à
( )
−
→ 2
.1lim
1
x
tgx
x
π
=
−
−
→
22
22
2
lim
1
x
x
tg
x
ππ
ππ
π =
( )
t
ttg
t 0
lim
2
→
π =
π
2
Fazendo uma mudança de variável,
temos :
→
→
−=
0
1
2 t
x
x
x
t
ππ
25.
( )x
x
x πsen
1
lim
2
1
−
→
= ? à
( )x
x
x πsen
1
lim
2
1
−
→
=
( )
( )x
x
x
x
ππ
πππ
−
−
+
→ sen.
1
lim
1
=
π
2
( )
x
x
xf
πsen
1 2
−
= =
( )( )
( )x
xx
ππ −
+−
sen
1.1
=
( )
( )x
x
x
−
−
+
1
sen
1
ππ
=
( )
( )x
x
x
−
−
+
1.
sen.
1
π
πππ
=
( )
( )x
x
x
ππ
πππ
−
−
+
sen.
1
26.
−
→
xgxg
x 2
cot.2cotlim
0
π
= ? à
−
→
xgxg
x 2
cot.2cotlim
0
π
= 0.∞
( )
−= xgxgxf
2
cot.2cot
π
= tgxxg .2cot =
xtg
tgx
2
=
xtg
tgx
tgx
2
1
2
−
=
tgx
xtg
tgx
.2
1
.
2
−
=
2
1 2
xtg−
−
→
xgxg
x 2
cot.2cotlim
0
π
=
2
1
lim
2
0
xtg
x
−
→
=
2
1
27.
x
xx
x 2
3
0 sen
coscos
lim
−
→
= 11102
2
1 ...1
lim
tttt
t
t +++++
−
→
=
12
1
−
( )
x
xx
xf 2
3
sen
coscos −
= = 12
23
1 t
tt
−
−
=
( )
( )( )11102
2
...1.1
1.
ttttt
tt
+++++−
−−
= 11102
2
...1 tttt
t
+++++
−
63.2
coscos xxt ==
→
→
1
0
t
x
xt cos6
= , xt 212
cos= , 122
1sen tx −=
6. Limites Trigonométricos Resolvidos
Sete páginas e 34 limites resolvidos
6
BriotxRuffini :
1 0 0 ... 0 -1
1 • 1 1 ... 1 1
1 1 1 ... 1 0
28.
xx
xx
x sencos
12cos2sen
lim
4
−
−−
→π
= ? à
xx
xx
x sencos
12cos2sen
lim
4
−
−−
→π
= ( )x
x
cos.2lim
4
−
→π
=
4
cos.2
π
− =
2
2
.2− =
2−
( )
xx
xx
xf
sencos
12cos2sen
−
−−
= =
( )
xx
xxx
sencos
11cos2cossen.2 2
−
−−−
=
xx
xxx
sencos
11cos2cos.sen.2 2
−
−+−
=
xx
xxx
sencos
cos2cos.sen.2 2
−
−
=
( )
xx
xxx
sencos
sencos.cos.2
−
−−
= xcos.2−
29.
( )
112
1sen
lim
1
−−
−
→
x
x
x
= ? à
( )
112
1sen
lim
1 −−
−
→ x
x
x
=
( )
( ) 1
112
.
1
1sen
.
2
1
lim
1
+−
−
−
→
x
x
x
x
= 1
( ) ( )
112
1sen
−−
−
=
x
x
xf =
( )
112
112
.
112
1sen
+−
+−
−−
−
x
x
x
x
=
( )
1
112
.
112
1sen +−
−−
− x
x
x
=
( )
( ) 1
112
.
1.2
1sen +−
−
− x
x
x
=
( )
( ) 1
112
.
1
1sen
.
2
1 +−
−
− x
x
x
30.
3
cos.21
lim
3
ππ
−
−
→ x
x
x
= ? à
3
cos.21
lim
3
ππ
−
−
→ x
x
x
=
−
−
+
→
2
3
2
3sen
.
2
3sen.2lim
3 x
x
x
x π
π
π
π
=
.
2
33sen.2
+ππ
= .
2
3
2
sen.2
π
= .
3
sen.2
π
= 3
2
3
.2 =
( )
3
cos.21
π
−
−
=
x
x
xf =
3
cos
2
1
.2
π
−
−
x
x
=
3
cos
3
cos.2
π
π
−
−
x
x
=
( )
−
−
−
+
−
2
3.2.1
2
3sen.
2
3sen2.2
x
xx
π
ππ
=
−
−
+
2
3
2
3sen.
2
3sen.2
x
xx
π
ππ
=
−
−
+
2
3
2
3sen
.
2
3sen.2
x
x
x
π
π
π
31.
xx
x
x sen.
2cos1
lim
0
−
→
= ? à
xx
x
x sen.
2cos1
lim
0
−
→
=
x
x
x
sen.2
lim
3
π
→
= 2
7. Limites Trigonométricos Resolvidos
Sete páginas e 34 limites resolvidos
7
( )
xx
x
xf
sen.
2cos1−
= =
( )
xx
x
sen.
sen211 2
−−
=
xx
x
sen.
sen211 2
+−
=
xx
x
sen.
sen.2 2
=
x
xsen.2
32.
xx
x
x sen1sen1
lim
0 −−+→
= ? à
xx
x
x sen1sen1
lim
0 −−+→
=
x
x
xx
x sen.2
sen1sen1
lim
0
−++
→
=
1.2
11+
=1
( )
xx
x
xf
sen1sen1 −−+
= =
( )
( )xx
xxx
sen1sen1
sen1sen1.
−−+
−++
=
( )
xx
xxx
sen1sen1
sen1sen1.
+−+
−++
=
( )
x
xxx
sen.2
sen1sen1. −++
=
x
x
xx
sen
.2
sen1sen1 −++
=
1.2
11+
= 1
33.
xx
x
x sencos
2cos
lim
0 −→
=
1
sencos
lim
0
xx
x
+
→
=
2
2
2
2
+ = 2
( )
xx
x
xf
sencos
2cos
−
= =
( )
( )( )xxxx
xxx
sencos.sencos
sencos.2cos
+−
+
=
( )
xx
xxx
22
sencos
sencos.2cos
−
+
=
( )
x
xxx
2cos
sencos.2cos +
=
( )
x
xxx
2cos
sencos.2cos +
=
1
sencos xx +
=
2
2
2
2
+ = 2
34.
3
sen.23
lim
3
ππ
−
−
→ x
x
x
= ? à
3
sen.23
lim
3
ππ
−
−
→ x
x
x
=
3
sen
2
3
.2
lim
3
ππ
−
−
→ x
x
x
=
3
sen
3
sen.2
lim
3
π
π
π
−
−
→ x
x
x
=
3
2
3cos.
2
3sen.2
lim
3
π
ππ
π
−
+
−
→ x
xx
x
=
3
3
2
3
3
cos.
2
3
3
sen.2
lim
3
π
ππ
π −
+
−
→
x
xx
x
=
( )
3
3.1
6
3
cos.
6
3
sen.2
lim
3
x
xx
x
−−
+
−
→
π
ππ
π
35. ?