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