image imagewidth (px) 26 336 | latex stringlengths 2 482 | split stringclasses 4
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\sin ^ { 2 } ( x ) + \cos ^ { 2 } ( x ) = 1
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\lim _ { x \rightarrow \infty } \int _ { 0 } ^ { x } e ^ { - y ^ { 2 } } d y = \frac { \sqrt { \pi } } { 2 }
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s = s _ { 0 } t + \frac { 1 } { 2 } a t ^ { 2 }
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h ^ { 0 }
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x ^ { 2 } + x + 1
| 2014 | |
A _ { 2 k } = \frac { 2 R A _ { k } } { 2 R + \sqrt { 4 R ^ { 2 } + A ^ { 2 } _ { k } } }
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[ \frac { 2 } { 3 } x ^ { \frac { 3 } { 2 } } ] _ { 0 } ^ { 1 }
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Y _ { d }
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\int ( n ) d w _ { m }
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x _ { n e w } = c ^ { \frac } { 1 } { 2 } x
| 2019 | |
( a - 2 x ) ( a + 2 x )
| 2014 | |
q = 1 + \alpha ( 1 - \cos \theta )
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x < \frac { c - b } { a }
| train | |
\beta = \cos ( \theta )
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x ^ { 3 } + 3 x ^ { 2 } \sqrt { 3 } - 3 x - \sqrt { 3 }
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\beta = \frac { v } { c } = \frac { b } { a }
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z _ { 1 } ^ { 2 } + 1 ^ { z } - z _ { 2 } ^ { 2 } + 2 ^ { z }
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f ( i )
| train | |
V + V _ { b }
| train | |
\frac { \beta + \gamma } { \theta }
| train | |
[ \tan G ]
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\sin x = \sin ( x + 2 \pi k )
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3 + 7 + 1 2 7 = 1 3 7
| 2019 | |
2 \log ( n ) = \log ( n ) ^ { 2 }
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\frac { 2 } { \frac { 1 } { x } + \frac { 1 } { y } }
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s = s _ { 0 } t + \frac { 1 } { 2 } a t ^ { 2 }
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( G )
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X _ { 2 } = - \frac { 4 9 } { 4 }
| train | |
\lim _ { r \rightarrow \infty } w ( r ) = 0
| 2019 | |
\pm \sqrt { - 1 }
| 2016 | |
- 2 + \frac { v - 2 } { v } \log ( 1 - v )
| 2016 | |
C = - m \cos a
| 2019 | |
- a _ { p - 1 } + 2 a _ { p } - a _ { p + 1 } + X = 0
| 2019 | |
6 9
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x ^ { k } t ( x ) d x
| 2019 | |
e
| train | |
\sqrt { 1 + \sqrt { 2 + \sqrt { 3 + \sqrt { 4 } } } }
| train | |
R ( N )
| train | |
B + j ^ { A }
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a _ { n } = a _ { 1 } \cdot q ^ { n - 1 }
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\lim _ { n \rightarrow \infty } \frac { 1 } { n ^ { p } } = 0
| train | |
\sqrt { - 1 }
| 2014 | |
\pi _ { 1 } ( X , q )
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\lim _ { n \rightarrow \infty } | x _ { n + 1 } - x _ { n } |
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a ( t ) = \int a ^ { ( 1 ) } d t = \int a _ { 0 } ^ { ( 1 ) } d t
| 2014 | |
x > A
| 2014 | |
[ n ]
| train | |
p = \frac { 1 } { \theta + 1 }
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\frac { ( s ^ { 2 } + t ^ { 2 } + u ^ { 2 } ) ^ { 2 } } { s t u }
| 2019 | |
\lim _ { x \rightarrow \frac { 1 } { 4 } } \frac { 1 - 4 ^ { x - \frac { 1 } { 4 } } } { 1 - 4 x }
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x = \frac { - b \pm \sqrt { b ^ { 2 } - 4 a c } } { 2 a }
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k _ { 1 } = k _ { t } = k
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n ^ { z - R }
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2 . 9
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- \frac { 9 } { 7 6 8 }
| 2019 | |
( a ) ^ { - 1 } - 1
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x ^ { 5 } + c x ^ { 3 } + d x ^ { 2 } + e x + f
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\sum _ { i } p _ { i } = \sum _ { i } p _ { i } ^ { 2 } = 1
| 2019 | |
Y = A X ^ { 2 }
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P ( x ) = \sum _ { i = 0 } ^ { n } a _ { j } x ^ { j }
| train | |
\int _ { 0 } ^ { \pi } \frac { d \theta } { a + b \cos \theta } = \frac { \pi } { \sqrt { a ^ { 2 } - b ^ { 2 } } }
| 2019 | |
\log _ { 2 } 8 + \log _ { 3 } 9 + \log _ { 4 } 1 6
| train | |
[ N ]
| train | |
a ^ { b ^ { c ^ { d } } }
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x _ { 1 } = \frac { ( 1 - \frac { 2 } { \sqrt { N - 1 } } ) N } { L }
| train | |
2 \alpha + 3 \sqrt { \beta }
| train | |
P = \sum p
| 2016 | |
( \sin ( x ) ^ { 2 } + 3 \cos ( x ) ^ { 2 } ) ^ { 4 }
| train | |
2 ( - 1 ) ^ { a b } + ( - 1 ) ^ { a + b } = ( - 1 ) ^ { a } + ( - 1 ) ^ { b } + 1
| 2016 | |
\frac { \int B d j } { g - j }
| train | |
- 1 . 5
| train | |
\phi ( s )
| train | |
- N X
| train | |
\sin ( \pi - \theta ) = \sin ( \theta )
| train | |
C
| train | |
k ^ { 3 } + 1 4 k ^ { 2 } - 1 3 2 k + 1 7 8 9
| train | |
f ( x ) = a _ { n } x ^ { n } + a _ { n - 1 } x ^ { n - 1 } + \cdots + a _ { 1 } x + a _ { 0 }
| train | |
A = \sqrt { a + \frac { 1 } { \sqrt { a + \frac { 1 } { \sqrt { a } } } } } + \sqrt { b }
| train | |
e ^ { - \alpha \sqrt { 1 - e ^ { 2 } } x ^ { 0 } }
| 2019 | |
V = a \cdot b \cdot c
| train | |
2 \int R _ { a b } R ^ { a b } c
| 2019 | |
y _ { 1 } ( x )
| train | |
2 ^ { 7 0 }
| train | |
r _ { k } = \frac { \int _ { t _ { k } } ^ { t _ { k + 1 } } x p _ { X } ( x ) } { \int _ { t _ { k } } ^ { t _ { k + 1 } } p _ { X } ( x ) }
| train | |
\sum _ { i = 1 } ^ { \infty } a _ { i } = 3
| train | |
x _ { 1 } + x _ { 2 } = x _ { 3 }
| train | |
\sum _ { n = 0 } ^ { \infty } f _ { n } ( x )
| train | |
\log _ { 2 } 8 = 3
| train | |
[ \sqrt { \sin ^ { r } v } ^ { u + B E } ]
| train | |
( x - 2 )
| train | |
6 0 - 1 3 6 \geq - 7 6
| train | |
\int _ { a } ^ { b } \frac { \sqrt { x } } { 2 } d x
| train | |
\sum _ { u \geq x } X - p
| train | |
b = c \sin B = c \cos A
| train | |
\frac { 2 \tan \alpha } { 1 - \tan ^ { 2 } \alpha }
| train | |
F ( x ) = \log | x | + 2
| train | |
a = 0 , 1
| train | |
\frac { 3 x } { 3 } + \frac { 1 } { 3 } = \frac { 4 } { 3 }
| 2014 | |
a = b + 1
| train | |
\frac { 1 } { 2 } ( 1 \pm i )
| train |
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