image imagewidth (px) 172 515 | latex stringlengths 5 309 |
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z _ { 1 } = r _ { 1 } ( \cos \theta _ { 1 } + i \sin \theta _ { 1 } ) | |
\log z = \log r + i ( \theta + 2 n \pi ) | |
( 6 9 + 1 7 7 \times 1 3 6 ) + ( 1 1 7 \div 1 4 0 ) > 5 6 1 2 | |
x ^ { 2 } \frac { d ^ { 2 } y } { d x ^ { 2 } } - 3 x \frac { d y } { d x } + y = \frac { \log x \cdot \sin { \log x } + 1 } { x } | |
p ^ { 3 } - ( x ^ { 2 } + x y + y ^ { 2 } ) p ^ { 2 } + ( x ^ { 3 } y + x ^ { 2 } y ^ { 2 } + x y ^ { 3 } ) p - x ^ { 3 } y ^ { 3 } = 0 | |
y = x p + \sqrt { b ^ { 2 } + a ^ { 2 } p ^ { 2 } } | |
( ( 2 4 - 4 4 ) \times 6 1 ) - ( 6 4 \div ( 1 9 6 + 1 6 2 ) ) > - 9 9 2 | |
\phi ( x ) | |
\log _ { c } ( a - b ) = \log _ { c } ( c ^ { ( \log _ { c } a - \log _ { c } b ) } - 1 ) + \log _ { c } b | |
1 5 1 \pm 1 4 3 \div 9 7 | |
2 1 - 5 \sqrt { 2 1 } + ( 1 5 \sqrt { 7 } - 2 1 \sqrt { 3 } ) i | |
7 8 \pm 5 \times 4 7 | |
\cos ( a + b ) = \cos a \cos b - \sin a \sin b | |
e ^ { - 1 } | |
1 - 1 + 1 - 1 + \ldots | |
2 ^ { n } - 1 | |
1 \pm 2 0 - 1 7 3 | |
\frac { 2 } { 3 } n ^ { 3 } | |
a ^ { 2 } - 2 a b | |
\cos x + i \sin x = e ^ { i x } | |
y = y _ { 0 } + t ^ { m } Y | |
b _ { n } - a _ { n } | |
1 7 5 \times ( 1 6 2 \times 1 0 3 ) \leq 2 9 2 0 0 5 0 | |
a ^ { 2 } - 2 a b = ( a - b ) ^ { 2 } - b ^ { 2 } | |
\gamma _ { j k } | |
1 1 3 + ( 1 6 8 \div 8 6 ) \leq 1 1 5 | |
b = a ^ { 2 } + c ^ { 2 } | |
n ^ { 2 } - n + 4 1 | |
n ^ { \log _ { 2 } ( 3 ) } | |
4 2 - 8 5 - 1 8 \geq - 2 5 | |
Y = g ( X ) = \frac { 1 } { X } | |
7 6 \pm ( ( 4 1 + 1 1 8 ) \times 1 2 4 ) \times 1 3 0 | |
a x ^ { 2 } + 2 b x + c = 0 | |
\gamma = 1 + \frac { 1 } { n } | |
9 4 + 7 4 + 6 + 1 3 8 > 2 1 | |
x ^ { 3 } + 3 x ^ { 2 } \sqrt { 3 } - 3 x - \sqrt { 3 } | |
( 2 9 - 2 4 + 1 6 9 ) \times 8 8 \leq - 1 4 4 3 1 | |
y _ { 1 } ( x ) = x ^ { 2 } | |
8 9 \times ( ( 1 5 5 \times 5 0 ) \div 1 3 2 ) \neq - 1 3 7 2 | |
\sin ( n x ) | |
1 2 + 1 3 8 + 1 4 4 + 7 3 > 4 5 | |
\sin ^ { 2 } ( x ) | |
( ( 8 4 / 1 1 3 ) / 5 1 ) - 1 1 9 = - 1 1 8 . 9 9 | |
\forall x , f ( x ) | |
a _ { 2 } = - 1 | |
2 4 / 1 2 5 = 0 . 1 9 | |
n _ { 1 } + \ldots + n _ { j } | |
4 \div 1 8 2 = 0 . 0 2 | |
4 , 2 , 1 | |
( - a ) ^ { n } = a ^ { n } | |
y = \frac { 1 } { Y } | |
( ( 1 1 6 - 1 7 ) \times ( 1 2 4 - 9 8 ) ) \div 1 0 > 2 0 5 | |
x ^ { - 4 } | |
\frac 1 { n ^ { k + 2 } } | |
\cos ( 4 a ) = 8 \cos ^ { 4 } ( a ) - 8 \cos ^ { 2 } ( a ) + 1 | |
( 1 8 + 2 2 ) \div 9 2 \neq 0 | |
y = x ^ { n } | |
\frac { y _ { 2 } x _ { 2 } - y _ { 1 } x _ { 1 } } { n } | |
3 = \sqrt { 6 + \sqrt { 6 + \sqrt { 6 + \sqrt { 6 + \ldots } } } } | |
\frac { n ( n + 1 ) } { 2 } + \frac { n ( n - 1 ) } { 2 } | |
1 4 \times 8 7 \neq - 1 9 6 | |
y \neq x | |
x ^ { 2 } + 2 x \sqrt { 2 } + 1 | |
1 4 8 - 1 4 1 \neq - 4 | |
\frac { 9 } { 5 } | |
k _ { n } = 1 | |
1 2 \div 7 5 \geq 0 | |
- \frac { 1 } { \pi } | |
( 2 - 1 ) | |
1 2 6 - 4 8 = 7 8 | |
( ( 2 6 \div 1 2 8 ) + 5 0 ) - ( 1 8 3 \div 2 9 ) \neq - 6 | |
1 0 ^ { 6 4 } | |
2 ^ { 1 7 } | |
( ( 1 2 6 \div 1 8 5 ) \times ( 5 9 + 1 3 9 ) ) - 5 9 > 0 | |
r = \sqrt { \theta } | |
n ^ { 3 } = n ^ { \log _ { 2 } 8 } | |
1 9 \times 7 \leq 1 3 3 | |
y = \frac { 1 } { x ^ { 2 } + 1 } | |
\sin ( x ) | |
2 6 \pm ( 1 0 9 + 1 1 9 - 8 2 ) \div ( ( 1 6 9 - 1 2 3 ) + ( 2 0 \div 1 7 5 ) ) | |
z ^ { 2 } - 2 z - 1 = 0 | |
1 8 6 \pm 6 + 9 8 + 1 7 6 + 9 2 | |
2 ^ { 1 8 } | |
f ( x ) = X ^ { 2 } - 4 X - 5 | |
m _ { 1 } , m _ { 2 } , m _ { 3 } | |
1 5 \div ( ( 7 6 \div 1 0 ) + ( 1 9 9 - 8 9 ) ) > 0 | |
\frac { 4 } { 3 } | |
b = \sqrt { 2 } | |
6 9 + ( ( 1 1 2 - 4 6 ) / 1 2 6 ) > 6 1 | |
x ^ { 5 } + x + a | |
( g ^ { - 1 } ) ^ { i j } | |
f + g | |
- 2 x | |
6 7 - 1 3 2 - 1 8 1 - 1 9 4 = - 5 2 | |
2 ^ { 5 0 } | |
( ( 1 1 7 \times 5 4 ) \div ( 1 4 1 \times 1 2 4 ) ) - ( ( 7 0 \div 1 9 3 ) \div 1 5 9 ) \geq 0 | |
2 { k } { \pi } | |
( 1 6 6 + ( 9 3 \times 6 7 ) ) - ( 6 4 + 1 2 7 + 1 7 6 ) \leq 6 0 3 0 | |
y ( 0 ) = \alpha _ { 1 } | |
2 ^ { 5 } + 2 + 1 |
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