Mathematische Formeln
L = lim | x | → ∞ cos 1 x ⋅ − 1 x 2 − 1 x 2 = lim | x | → ∞ cos 1 x ⋅ − 1 x 2 ⋅ x 2 − 1 = cos 1 ∞ = cos 0 = 1 {\displaystyle {\begin{aligned}L&=\lim _{|x|\to \infty }\ {\frac {\cos {\frac {1}{x}}\cdot {\frac {-1}{x^{2}}}}{\frac {-1}{x^{2}}}}\\&=\lim _{|x|\to \infty }{\cos {\frac {1}{x}}}\cdot {\frac {-1}{x^{2}}}\cdot {\frac {x^{2}}{-1}}\\&=\cos {\frac {1}{\infty }}=\cos 0=1\end{aligned}}}
Chemische Reaktionsgleichungen
C H 3 C O O H + C H 3 O H ⟶ C H 3 C O O C H 3 ↑ + H 2 O {\displaystyle \mathrm {CH_{3}COOH+CH_{3}OH\longrightarrow CH_{3}COOCH_{3}\uparrow +H_{2}O} } S d p : 118 ∘ C 65 ∘ C 57 ∘ C 100 ∘ C {\displaystyle _{Sdp:\quad 118\,^{\circ }C\qquad 65\,^{\circ }C\qquad \qquad \qquad 57\,^{\circ }C\qquad \quad 100\,^{\circ }C}}
Physikalische Formeln
α = K c 2 ⋅ c 0 ( 1 + 4 ⋅ c 0 K c − 1 ) {\displaystyle \alpha ={\frac {K_{c}}{2\cdot c_{0}}}{\biggl (}{\sqrt {1+{\frac {4\cdot c_{0}}{K_{c}}}-1}}{\biggr )}} Ostwaldsches Verdünnungsgesetz
Ostwaldsches Verdünnungsgesetz