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Dresden Database Research Group 11

e^x = \sum_{n=0}^\infty x^n/n! > \tfrac{1}{n!}\cdot x^n

-z\cdot (\epsilon + g) = (g + \epsilon)\cdot (-z)

2/3\cdot \frac71 = 2\cdot \frac13/(\tfrac{1}{7})

\frac{3*5}{2}8 = 60

\frac{\frac{1}{6}}{\frac16 + 5 \cdot \dfrac16/7} = 7/12

\cos{13\cdot \pi/12} = \frac{1}{4}\cdot \left(-\sqrt{6} - \sqrt{2}\right)

z \Rightarrow (z^2 - 3 \cdot z + 1)^2 - 3 \cdot (z^2 - 3 \cdot z + 1) + 1 = z^2 - 3 \cdot z + 1 = z

\alpha x^9 \cdot \left(x + 1\right) = x^9 \alpha + \alpha x^{10}

x x + z^2 \alpha^2 + \alpha z x*2 = (x + z \alpha)^2

3*3! = 18

\left( 5, 9, 0\right) = ( x, y, \nu) + ( 2, 1, -5) \Rightarrow ( 2 + x, 1 + y, \nu + 5 \cdot (-1)) = \left( 5, 9, 0\right)

(1 + z + z^2)^n = (\frac{1 - z^3}{1 - z})^n = \left(1 - z^3\right)^n \cdot \left(1 - z\right)^{-n}

0.48\cdot 23.9 = 11.472

49*(-1) - 7*k = -7*7 - k*7

\frac{1}{2} \cdot m = \frac{1}{2^m} \cdot 2^{m + (-1)} \cdot m

k + 1 + n + 1 = k + n + 1 + 1

(e^{i\cdot \theta})^n = e^{i\cdot n\cdot \theta} = \cos{n\cdot \theta} + i\cdot \sin{n\cdot \theta}

\frac{1}{41} \cdot (72 + 8 \cdot i - 90 \cdot i + 10) = (82 - 82 \cdot i)/41 = 2 - 2 \cdot i

(f\cdot b)^{i + 2} = f^{i + 2}\cdot b^{i + 2} = f^{i + 1}\cdot f\cdot b^{i + 1}\cdot b

3 \left((-1) + x x\right) + 4 = 1 + x^2 \cdot 3

2 \times 2^k = 2^{k + 1} \times ...

3/51*4/52 + 4/51*\frac{48}{52} = \frac{1}{52}*4

\frac{24}{24 + 10} = \frac{1}{34} \cdot 24 = \frac{12}{17}

b*e*b = b*e*b

x^l = \left((x^{1/q})^q\right)^l = (x^{1/q})^{q \cdot l}

(3\cdot z + 1)\cdot (1 + z)^4 = 1 + 7\cdot z + 18\cdot z^2 + z \cdot z^2\cdot 22 + 13\cdot z^4 + 3\cdot z^5

(z + 2*(-1))^2 + h = (z + 2*\left(-1\right))*(z + 2*(-1)) + h = z * z - 4*z + 4 + h

x^2 + x*b \Rightarrow -(\frac{1}{2}*b)^2 + (x + b/2) * (x + b/2)

(b + 1) \times (b + 1) = b \times b + 2 \times b + 1 = b^2 + 1 = b^1 + 1 - b \times b + b + 1 = -b = -b = b

k \cdot y = (k + 0) \cdot y = k \cdot y + 0 \cdot y

0 = p^2 \implies p = 0

2\times (\arctan(\infty) - \arctan\left(-\infty\right)) = 2\times \pi

e^{Y + R} = e^R e^Y \implies 0 = (R, Y)

\dfrac{1 - r^{n + 1}}{1 - r} = \frac{1}{1 - r}*(1 - r^{1 + n})

1 + 3^{1 + k} = 1 + 3^k\cdot 3

B = \sqrt{B*A} \Rightarrow 0 = B\text{ or }B = A

\theta = \frac{180}{\pi} \cdot \theta \cdot \tfrac{1}{180} \cdot \pi

h > -1 rightarrow 0 < 1 + h

20^2 + 21 \cdot 21 = 29^2

\frac{1}{0 (-1) + 1} = 1

\cos(f_1 + f_2) = \cos(f_1) \cdot \cos(f_2) - \sin(f_1) \cdot \sin(f_2)

6*4*z^2*9 = 24*9*z * z = 216*z^2

\mathbb{E}(Z) = \mathbb{E}(\sum_{i=1}^l Z_i) = \sum_{i=1}^l \mathbb{E}(Z_i)

\frac{1}{12}*\left(2^6 + 8*2^2 + 3*2^2*2^2\right) = 12

4^{2n} + (-1) = 16^n + (-1) = (16 + (-1)) (16^{n + (-1)} + 16^{n + 2(-1)} + ... + 1)

-5/4 \cdot 2 = -5/2

(b \cdot \tfrac{a}{b})^2 = b \cdot a \cdot b \cdot \frac{a}{b}/b = b \cdot \frac{a^2}{b}

((1 + x)^l)^2 = \left(1 + x\right)^{2l}

\dfrac{1}{f\cdot 4}\cdot (\vartheta\cdot f\cdot 4 + f^2\cdot y^2\cdot 4 + 4\cdot f\cdot U\cdot y) = \vartheta + f\cdot y^2 + y\cdot U

e^t = 1 + t + t^2/2! + \dotsm > \frac{t^2}{2}

8.712*0.01 = \frac{1}{100} 8.712

\cos(π\times 2 - v) = \cos(-v + 4\times π)

\frac{1}{80 \cdot y} \cdot (y \cdot 70 + 60) = 10/10 \cdot \frac{y \cdot 7 + 6}{y \cdot 8}

-7 - i\cdot 17 = 3 + 10\cdot (-1) - i\cdot 17

p^9 = (p^3)^3 = (p + 1)^3 = p * p * p + 1 = p + 2 = p + (-1)

{l \choose l - k} = {l \choose k}

\pi/6 + 3/2\cdot \pi = \pi\cdot 5/3

\frac{8}{4} \cdot \frac{r^3}{r^4} = \frac{r^3 \cdot 8}{4 \cdot r^4}

\frac{y^2 + 5\cdot y + 3}{y^2 + y + 3} = 1 + \tfrac{4\cdot y}{y^2 + y + 3} \approx 1 + \frac{4}{y}

\dfrac{36\cdot (-1) + y^2 - 5\cdot y}{4\cdot y + y \cdot y} = \dfrac{1}{(4 + y)\cdot y}\cdot (4 + y)\cdot (9\cdot \left(-1\right) + y)

\frac{3}{5}\cdot l = \frac{1}{100}\cdot 60\cdot l

\beta^2 - \beta + 1 = 0 = \beta^3 + 2 \cdot \beta + 1\Longrightarrow \beta^2 = \beta \cdot \beta^2

\frac{s \cdot 42}{s \cdot (-24)} \cdot 1 = -\frac74 \cdot \frac{(-6) \cdot s}{s \cdot (-6)}

(\omega + b)\cdot g = g\cdot \omega + g\cdot b

((1 + x)^{1/2} x + y) (-x*\left(x + 1\right)^{1/2} + y) = -x^2 + y^2 - x^3

\left(z + 3\right)^{1 / 2} (z + 5 \left(-1\right))^{1 / 2} = (\left(z + 3\right) (z + 5 (-1)))^{1 / 2} = (z z - 2 z + 15 (-1))^{1 / 2} = (\left(z + (-1)\right)^2 - 4^2)^{\tfrac{1}{2}}

26 + 9\left(-1\right) = 17

11/6 \pi + 3/4 \pi = \pi \frac{31}{12}

w\times x\times 3 + 15\times \left(-1\right) = 0 \Rightarrow x = 5/w

\frac{8}{1/3}\frac{1}{27} = 8/9

5 + x*30 = 5 + x*2*3*5

v\cdot f_2 + b_2\cdot u + v\cdot f_1 + b_1\cdot u = u\cdot \left(b_2 + b_1\right) + v\cdot (f_1 + f_2)

\frac{1}{(1 - x)^2} \cdot (1 + x^{m + 1} \cdot m - x^m \cdot (m + 1)) = 1 + x \cdot 2 + 3 \cdot x^2 + \dots + x^{m + (-1)} \cdot m

g \cdot g \cdot h = h \cdot g \cdot g

\frac{1}{x \cdot 3 + 6} \cdot (20 + 10 \cdot x) = \frac{10}{3} \cdot \frac{1}{x + 2} \cdot (2 + x)

\left(1 + 2 + 3 + 4 + 5\right)*60/5*111 = 19980

\frac{d^5}{d^5} \cdot \dfrac{1}{55} \cdot 44 = \dfrac{44 \cdot d^5}{d^5 \cdot 55}

0 - -1 = \left(-1\right) \cdot \left(-1\right)

\tan{3 \cdot \theta} = -\tfrac{\tan{\theta} + \tan{2 \cdot \theta}}{1 - \tan{\theta} \cdot \tan{2 \cdot \theta}} = -\tan(\theta + 2 \cdot \theta) = \tan{-3 \cdot \theta}

2 - x^2 - z^2 = x^2 \Rightarrow x \cdot x + z^2/2 = 1

\pi \dfrac{1}{12}17 - \frac{23}{12} \pi = -\frac{\pi}{2}

(-3) \cdot (-3) = 9

|\frac{1}{jd + b}| = \frac{1}{|dj + b|}

\tanh{x} = \sinh{x}/\cosh{x} = \frac{1}{1 + e^{-2*x}}*(1 - e^{-2*x})

\dfrac145 + \frac{1}{2}5 = \dfrac{15}{4}

\sigma^2 + x^2 - \sigma\cdot x\cdot 2 = (x - \sigma)^2

\frac{6}{2\cdot (q + 2)\cdot (7 + q)} = \frac{3}{\left(q + 2\right)\cdot (q + 7)}\cdot \frac22

\frac{1}{k^3}\cdot k \cdot k = 1/k

7 + 14*z + 7*z * z = 7*\left(1 + 2*z + z^2\right) = 7*\left(1 + z\right)^2

\cos^2(r) - \sin^2(r) = \cos(r\cdot 2)

\frac{1}{-32 k + 28 (-1)}(20 + 40 k) = 4/4 \frac{1}{7(-1) - 8k}\left(k\cdot 10 + 5\right)

39 * 39 + 52^2 = 65 * 65 = 25 * 25 + 60 * 60

-\frac{3}{4}\cdot \left(-3/4\right) = 9/16

27/9 = \frac{27\cdot \tfrac{1}{9}}{9\cdot \frac19} = 3/1 = 3

12 \times 12 \times 12 + 1 \times 1 \times 1 = 1729

(9\cdot x^4 + 10)\cdot (9\cdot x^4 + 10\cdot (-1)) = (x^4\cdot 9)^2 - 10^2

\frac{28 \cdot 3}{28 \cdot 2} = \tfrac{84}{56}

\frac{1}{(a + 9) (a + 3(-1))} = \dfrac{1}{27 (-1) + a^2 + a*6}

-z*(-J) = J*z

\dfrac{1}{\cos(x)*(1 + \sin\left(x\right))}*(2 + 2*\sin(x)) = \frac{1}{\cos(x)}*2 = 2*\sec(x)