style="background: #ececec; color: black; font-weight: bold; vertical-align: middle; text-align: left; " class="table-rh" style="background: #ececec; color: black; font-weight: bold; vertical-align: middle; text-align: left; " class="table-rh" வார்ப்புரு:Rule வார்ப்புரு:Dhr 5
வார்ப்புரு:X-larger ★
<poem>
ஜெயரத்தினா விக்கியிடை இணைப்புக் கருவி
{{{{catdiffuse -துணைப்பகுப்புகள் சேர்க்கப்பட வேண்டும்.
{{Close paraphrasing
{{citation style
வார்ப்புரு:Multiple issues| வார்ப்புரு:cleanup|reason=General copyediting needed|date=August 2015}}
வார்ப்புரு:one source|date=August 2015}}
வார்ப்புரு:Orphan|date=August 2015}}
வார்ப்புரு:Multiple issues| {{unreferenced|date=April 2015}}
{{Notability|date=September 2019}}
வார்ப்புரு:container category வார்ப்புரு:Non-free image data
|Description = Movie Poster
|Source = Anand Movie Land
|Article = Vasuki (film)
|Portion = Film poster only.
|Low_resolution = Sufficient resolution for illustration, but considerably lower resolution than original.
|other_information = Owned by Anand Movie Land.
}}
படிமத் தொகுப்பு: <gallery mode="packed-hover" heights="100">-----</gallery>
வார்ப்புரு:One source|section (வேள்விக்குடி செப்பேடுகள்)
படிமம்:சுவரொட்டி-மோகினி; நபர்:குமுதினி
" வார்ப்புரு:citation style
வார்ப்புரு:nowikidatalink மேற்கோள்
[ 1] [ 2]
சிவப்பு
f
(
x
)
=
log
2
(
x
)
{\displaystyle {\color {Blue}f(x)}={\color {Blue}\log _{2}(x)}}
∑
n
=
1
∞
{\displaystyle \sum _{n=1}^{\infty }}
தீமை ,
---
வார்ப்புரு:Non-free promotional
வார்ப்புரு:coord|*|*|display=title
தொகு
a
sin
α
=
b
sin
β
=
c
sin
γ
=
2
R
.
{\displaystyle {\frac {a}{\sin {\alpha }}}={\frac {b}{\sin {\beta }}}={\frac {c}{\sin {\gamma }}}=2R.}
(
x
+
y
)
n
=
∑
k
=
0
n
(
n
k
)
x
n
−
k
y
k
{\displaystyle (x+y)^{n}=\sum _{k=0}^{n}{\binom {n}{k}}x^{n-k}y^{k}}
( ∗ )
⋯
{\displaystyle \cdots }
G
⊕
H
{\displaystyle G\oplus H}
⊗
{\displaystyle \otimes }
1
◻
2
{\displaystyle {1\square 2}}
≡ ∗ ⇒ , ⇔ , → x = 3 ⁄2 A > B, B > C எனில், A > C A ≥ B, B ≥ C எனில், A ≥ C
A < B, B < C எனில், A < C
A ≤ B, B ≤ C எனில், A ≤ C
⏟
{\displaystyle \underbrace {\qquad \qquad \qquad \qquad \qquad \qquad } _{}}
ln
(
a
b
)
=
∫
1
a
b
1
x
d
x
=
∫
1
a
1
x
d
x
+
∫
a
a
b
1
x
d
x
=
∫
1
a
1
x
d
x
+
∫
1
b
1
a
t
d
(
a
t
)
=
∫
1
a
1
x
d
x
+
∫
1
b
1
t
d
t
=
ln
(
a
)
+
ln
(
b
)
.
{\displaystyle {\begin{aligned}\ln(ab)=\int _{1}^{ab}{\frac {1}{x}}\;dx&=\int _{1}^{a}{\frac {1}{x}}\;dx\;+\int _{a}^{ab}{\frac {1}{x}}\;dx\\&=\int _{1}^{a}{\frac {1}{x}}\;dx\;+\int _{1}^{b}{\frac {1}{at}}\;d(at)\\&=\int _{1}^{a}{\frac {1}{x}}\;dx\;+\int _{1}^{b}{\frac {1}{t}}\;dt\\&=\ln(a)+\ln(b).\end{aligned}}}
உள்ளிடு கோப்பு
உள்ளிடு கோப்பு அல்ல
±i
θ, 90o , Σ,
60
∘
{\displaystyle 60^{\circ }}
P
∝
1
V
{\displaystyle P\propto {\frac {1}{V}}}
∵
{\displaystyle \because \,}
a
∼
b
{\displaystyle a\sim b}
[
a
]
=
{
b
∈
A
|
a
∼
b
}
{\displaystyle [a]=\{b\in A|a\sim b\}}
a
≡
b
(
mod
n
)
{\displaystyle a\equiv b{\pmod {n}}}
சமன்பாடு (2
23
88
{\displaystyle 23{\mbox{ }}88}
(
2
)
{\displaystyle \qquad \qquad (2)}
Δ
{\displaystyle \Delta }
y
˙
{\displaystyle {\dot {y}}}
y
¨
{\displaystyle {\ddot {y}}}
Re
(
−
3.5
+
2
i
)
=
−
3.5
Im
(
−
3.5
+
2
i
)
=
2
{\displaystyle {\begin{aligned}\operatorname {Re} (-3.5+2i)&=-3.5\\\operatorname {Im} (-3.5+2i)&=2\end{aligned}}}
(
R
=
b
2
a
)
{\displaystyle \left(R={\frac {b^{2}}{a}}\right)}
e
i
∗
∈
E
∗
,
v
j
∗
∈
e
i
∗
{\displaystyle e_{i}^{*}\in E^{*},~v_{j}^{*}\in e_{i}^{*}}
d
d
x
(
1
g
(
x
)
)
=
d
d
x
(
f
(
x
)
g
(
x
)
)
{\displaystyle {\frac {d}{dx}}\left({\frac {1}{g(x)}}\right)={\frac {d}{dx}}\left({\frac {f(x)}{g(x)}}\right)}
=
f
′
(
x
)
g
(
x
)
−
f
(
x
)
g
′
(
x
)
(
g
(
x
)
)
2
{\displaystyle ={\frac {f'(x)g(x)-f(x)g'(x)}{(g(x))^{2}}}}
=
0
⋅
g
(
x
)
−
1
⋅
g
′
(
x
)
(
g
(
x
)
)
2
{\displaystyle ={\frac {0\cdot g(x)-1\cdot g'(x)}{(g(x))^{2}}}}
=
−
g
′
(
x
)
(
g
(
x
)
)
2
.
{\displaystyle ={\frac {-g'(x)}{(g(x))^{2}}}.}
A
∩
B
=
∅
.
{\displaystyle A\cap B=\varnothing .\,}
{
1
,
3
}
⊂
{
1
,
2
,
3
,
4
}
{\displaystyle \{1,3\}\subset \{1,2,3,4\}}
ord
(
a
b
)
=
ord
(
b
a
)
{\displaystyle \operatorname {ord} (ab)=\operatorname {ord} (ba)}
⊆
{\displaystyle \subseteq }
A ⊊ B
0
→
{\displaystyle {\vec {0}}}
g
H
=
{
g
h
:
h
∈
H
}
{\displaystyle gH=\{gh:h\in H\}}
H
∖
G
{\displaystyle H\backslash G}
n
≥
1
{\displaystyle n\geq 1}
g
1
2
+
f
1
2
−
c
1
{\displaystyle {\sqrt {g_{1}^{2}+f_{1}^{2}-c_{1}}}}
⇒
{\displaystyle \Rightarrow }
→
{\displaystyle \rightarrow }
⇔,
⇔
{\displaystyle \Leftrightarrow }
∀
a
∈
R
,
{\displaystyle \forall a\in \mathbb {R} ,}
|
a
|
=
{
a
,
if
a
≥
0
−
a
,
if
a
<
0.
{\displaystyle |a|={\begin{cases}a,&{\mbox{if }}a\geq 0\\-a,&{\mbox{if }}a<0.\end{cases}}}
A
1
=
∫
1
b
1
x
d
x
=
log
e
b
.
{\displaystyle A_{1}\;=\;\int _{1}^{b}{\frac {1}{x}}\,dx\;=\log _{e}b.}
a
∈
R
,
{\displaystyle a\in \mathbb {R} ,}
∞
{\displaystyle \infty }
(எதிர்ப்பக்கம்)2 + (அடுத்துள்ள பக்கம்)2 = (செம்பக்கம்)2
{
தலை,பூ
}
{\displaystyle \{{\text{தலை,பூ}}\}}
எதிர்ப்பக்கம்
{\displaystyle {\text{எதிர்ப்பக்கம்}}}
a ≠ 0, a ≥ 0
{
4
x
+
2
y
=
14
2
x
−
y
=
1.
{\displaystyle {\begin{cases}4x+2y=14\\2x-y=1.\end{cases}}\,}
X
=
log
a
b
=
ln
b
ln
a
,
{\displaystyle X=\log _{a}b={\frac {\ln b}{\ln a}},}
≠
{\displaystyle \not =}
a
>
0
{\displaystyle a>0}
X m /n a , m , n -முழு எண்கள்
X
=
a
n
m
=
(
a
m
)
n
{\displaystyle X={\sqrt[{m}]{a^{n}}}=\left({\sqrt[{m}]{a}}\right)^{n}}
X
=
±
a
n
m
=
±
(
a
m
)
n
{\displaystyle X=\pm {\sqrt[{m}]{a^{n}}}=\pm \left({\sqrt[{m}]{a}}\right)^{n}}
P
=
2
x
+
3
y
+
5
{\displaystyle {\color {BrickRed}P{=}2x+3y+5}}
Q
=
2
x
+
5
y
+
x
y
+
1
,
{\displaystyle {\color {RoyalBlue}Q{=}2x+5y+xy+1},}
P
Q
=
(
2
x
⋅
2
x
)
+
(
2
x
⋅
5
y
)
+
(
2
x
⋅
x
y
)
+
(
2
x
⋅
1
)
+
(
3
y
⋅
2
x
)
+
(
3
y
⋅
5
y
)
+
(
3
y
⋅
x
y
)
+
(
3
y
⋅
1
)
+
(
5
⋅
2
x
)
+
(
5
⋅
5
y
)
+
(
5
⋅
x
y
)
+
(
5
⋅
1
)
{\displaystyle {\begin{array}{rccrcrcrcr}{\color {BrickRed}P}{\color {RoyalBlue}Q}&{=}&&({\color {BrickRed}2x}\cdot {\color {RoyalBlue}2x})&+&({\color {BrickRed}2x}\cdot {\color {RoyalBlue}5y})&+&({\color {BrickRed}2x}\cdot {\color {RoyalBlue}xy})&+&({\color {BrickRed}2x}\cdot {\color {RoyalBlue}1})\\&&+&({\color {BrickRed}3y}\cdot {\color {RoyalBlue}2x})&+&({\color {BrickRed}3y}\cdot {\color {RoyalBlue}5y})&+&({\color {BrickRed}3y}\cdot {\color {RoyalBlue}xy})&+&({\color {BrickRed}3y}\cdot {\color {RoyalBlue}1})\\&&+&({\color {BrickRed}5}\cdot {\color {RoyalBlue}2x})&+&({\color {BrickRed}5}\cdot {\color {RoyalBlue}5y})&+&({\color {BrickRed}5}\cdot {\color {RoyalBlue}xy})&+&({\color {BrickRed}5}\cdot {\color {RoyalBlue}1})\end{array}}}
P
Q
=
4
x
2
+
21
x
y
+
2
x
2
y
+
12
x
+
15
y
2
+
3
x
y
2
+
28
y
+
5
.
{\displaystyle PQ=4x^{2}+21xy+2x^{2}y+12x+15y^{2}+3xy^{2}+28y+5\,.}
θ
=
arcsin
(
எதிர்ப்பக்கம்
/
செம்பக்கம்
)
{\displaystyle \theta =\arcsin({\text{எதிர்ப்பக்கம்}}/{\text{செம்பக்கம்}})\,}
90°
sin
θ
=
y
1
=
y
{\displaystyle \sin \theta \ ={\frac {y}{1}}=y\,}
θ
=
arcsin
(
எதிர்ப்பக்கம்
செம்பக்கம்
)
{\displaystyle \theta =\arcsin({\frac {\text{எதிர்ப்பக்கம்}}{\text{செம்பக்கம்}}})\,}
sin
(
−
θ
)
=
−
sin
θ
{\displaystyle \sin(-\theta )\ =-\sin \theta \,}
cos
(
−
θ
)
=
+
cos
θ
{\displaystyle \cos(-\theta )\ =+\cos \theta \,}
sin
2
θ
=
sin
2
(
−
θ
)
{\displaystyle \sin ^{2}\theta =\sin ^{2}(-\theta )\,}
sin
2
(
t
+
1
2
π
)
{\displaystyle \sin ^{2}\left(t+{\frac {1}{2}}\pi \right)}
sin
2
(
π
2
−
θ
)
{\displaystyle \sin ^{2}({\frac {\pi }{2}}-\theta )\,}
cot
2
(
π
2
−
θ
)
{\displaystyle \cot ^{2}({\frac {\pi }{2}}-\theta )\,}
a
h
,
{\displaystyle {\frac {a}{h}},\,}
(G , *)
f
(
u
∗
v
)
=
f
(
u
)
⊙
f
(
v
)
u
∈
G
,
v
∈
H
{\displaystyle f(u*v)=f(u)\odot f(v)u\in G,v\in H}
f
′
(
x
)
{\displaystyle f'(x)}
(
f
g
)
′
(
x
)
=
a
{\displaystyle (fg)'(x)=a}
f
′
′
(
x
)
<
0
{\displaystyle \ f^{\prime \prime }(x)<0}
f
:
(
a
,
b
)
→
R
{\displaystyle f\colon (a,b)\rightarrow \mathbb {R} }
f
′
(
c
k
)
=
0
{\displaystyle \ f^{\prime }(c_{k})=0}
(
g
∘
f
)
(
x
)
=
g
(
f
(
x
)
)
.
{\displaystyle (g\circ f)(x)=g(f(x)).\ }
f
′
(
x
)
=
0
{\displaystyle \ f^{\prime }(x)=0}
f
(
a
)
=
f
(
b
)
{\displaystyle \ f(a)=f(b)}
f
(
a
k
)
=
f
(
b
k
)
{\displaystyle \ f(a_{k})=f(b_{k})}
f
′
(
x
0
)
≠
0
{\displaystyle \displaystyle f'(x_{0})\neq 0}
f
′
(
x
)
=
g
′
(
x
)
=
0
{\displaystyle \ f^{\prime }(x)=g^{\prime }(x)=0}
f
(
x
)
=
c
o
s
3
π
x
x
,
{\displaystyle f(x)={\frac {cos3\pi x}{x}},\,}
c ∈ (a ,b )
c
∈
(
a
,
b
)
{\displaystyle c\in \ (a,b)}
f
(
x
,
y
)
=
x
2
+
y
2
(
1
−
x
)
3
,
x
,
y
∈
R
,
{\displaystyle f(x,y)=x^{2}+y^{2}(1-x)^{3},\qquad x,y\in \mathbb {R} ,}
f
{\displaystyle f\,}
[
−
r
,
r
]
{\displaystyle [-r,r]}
π
2
.
{\displaystyle {\frac {\pi }{2}}.}
f
(
x
)
=
x
3
3
−
x
,
{\displaystyle f(x)={\frac {x^{3}}{3}}-x,\,}
f
(
x
)
=
x
3
+
3
x
2
−
2
x
+
1
,
{\displaystyle f(x)=x^{3}+3x^{2}-2x+1,\,}
x 3 + 3x 2 − 2x + 1
f
(
x
)
=
x
2
{\displaystyle f(x)=x^{2}}
x
x
{\displaystyle {\sqrt[{x}]{x}}}
x 2
lim
p
→
0
∑
i
=
1
n
w
i
x
i
p
p
=
∏
i
=
1
n
x
i
w
i
{\displaystyle {\begin{aligned}&\lim _{p\to 0}{\sqrt[{p}]{\sum _{i=1}^{n}w_{i}x_{i}^{p}}}=\prod _{i=1}^{n}x_{i}^{w_{i}}\end{aligned}}}
M
p
(
b
x
1
,
…
,
b
x
n
)
{\displaystyle M_{p}(bx_{1},\dots ,bx_{n})}
b
M
p
(
x
1
,
…
,
x
n
)
{\displaystyle bM_{p}(x_{1},\dots ,x_{n})}
∑
i
=
1
n
w
i
x
i
q
≤
∏
i
=
1
n
x
i
w
i
⋅
q
≤
∑
i
=
1
n
w
i
x
i
q
{\displaystyle \sum _{i=1}^{n}w_{i}x_{i}^{q}\leq \prod _{i=1}^{n}x_{i}^{w_{i}\cdot q}\leq \sum _{i=1}^{n}w_{i}x_{i}^{q}}
∏
i
=
1
n
x
i
w
i
⋅
q
≤
∑
i
=
1
n
w
i
x
i
q
{\displaystyle \prod _{i=1}^{n}x_{i}^{w_{i}\cdot q}\leq \sum _{i=1}^{n}w_{i}x_{i}^{q}}
a
b
c
2
(
a
+
b
+
c
)
.
{\displaystyle {\frac {abc}{2(a+b+c)}}.}
H
=
(
h
a
−
1
+
h
b
−
1
+
h
c
−
1
)
/
2
{\displaystyle H=(h_{a}^{-1}+h_{b}^{-1}+h_{c}^{-1})/2}
B
=
B
0
{\displaystyle B=B_{0}}
B
{\displaystyle \ B}
A
{\displaystyle A}
S
{\displaystyle S}
r
R
=
a
b
c
2
(
a
+
b
+
c
)
.
{\displaystyle rR={\frac {abc}{2(a+b+c)}}.}
F
+
V
−
E
=
2.
{\displaystyle F+V-E=2.}
H
<
G
<
A
.
{\displaystyle H<G<A.}
வார்ப்புரு:Non-free promotional
பிறந்தார்[ 3]
வந்தார்.[ 3]
<ref>{{MathWorld |title=Cardinal Number |id=CardinalNumber }}</ref>
{{EB1911|wstitle=Andaman Islands}}
[https://ta.wikipedia.org/wiki/%E0%AE%AA%E0%AE%AF%E0%AE%A9%E0%AE%B0%E0%AF%8D:Booradleyp1/common.js]
![{\displaystyle [a]=\{b\in A|a\sim b\}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ecd447db4dc0435369173860cd769d704aab0a86)
![{\displaystyle X={\sqrt[{m}]{a^{n}}}=\left({\sqrt[{m}]{a}}\right)^{n}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c93ee35b63c3b583d5ac5392f4414960ca6e99ad)
![{\displaystyle X=\pm {\sqrt[{m}]{a^{n}}}=\pm \left({\sqrt[{m}]{a}}\right)^{n}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6c3de0f09a8f045a2a259e476c691ca30ab986b0)
![{\displaystyle [-r,r]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5dbcf3f99b353b618465500fe9576e0850885ffd)
![{\displaystyle {\sqrt[{x}]{x}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/61b4a0a76158849854a302fc639dfc882ec16008)
![{\displaystyle {\begin{aligned}&\lim _{p\to 0}{\sqrt[{p}]{\sum _{i=1}^{n}w_{i}x_{i}^{p}}}=\prod _{i=1}^{n}x_{i}^{w_{i}}\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a008d62699832a3f4521b1c97cd2a812e2ae465b)
![{\displaystyle G={\sqrt[{2}]{(2)(8)}},}](https://wikimedia.org/api/rest_v1/media/math/render/svg/129e21c2ac1d3f58eeeaa723ab5281e1b0950caf)
