( 4 3 ⋅ r ) 2 + r 2 {\displaystyle {\sqrt {\left({\frac {4}{3}}\cdot r\right)^{2}+r^{2}}}}
16 9 ⋅ r 2 + r 2 {\displaystyle {\sqrt {{\frac {16}{9}}\cdot r^{2}+r^{2}}}}
25 9 ⋅ r 2 {\displaystyle {\sqrt {{\frac {25}{9}}\cdot r^{2}}}}
5 3 ⋅ r {\displaystyle {\frac {5}{3}}\cdot r}
1 3 ⋅ π ⋅ r 3 ⋅ 4 3 {\displaystyle {\frac {1}{3}}\cdot \pi \cdot r^{3}\cdot {\frac {4}{3}}}
π ⋅ r 2 ⋅ h + 4 9 ⋅ π ⋅ r 3 {\displaystyle \pi \cdot r^{2}\cdot h+{\frac {4}{9}}\cdot \pi \cdot r^{3}}
h = 6 ⋅ π − 4 9 ⋅ π ⋅ r 3 π ⋅ r 2 = 6 r 2 − 4 9 ⋅ r {\displaystyle h={\frac {6\cdot \pi -{\frac {4}{9}}\cdot \pi \cdot r^{3}}{\pi \cdot r^{2}}}={\frac {6}{r^{2}}}-{\frac {4}{9}}\cdot r}
O ( r ) = π ⋅ r 2 + 12 π r − 8 9 ⋅ π ⋅ r 2 + 5 3 ⋅ π ⋅ r 2 = 16 9 ⋅ π ⋅ r 2 + 12 π r {\displaystyle O(r)=\pi \cdot r^{2}+{\frac {12\pi }{r}}-{\frac {8}{9}}\cdot \pi \cdot r^{2}+{\frac {5}{3}}\cdot \pi \cdot r^{2}={\frac {16}{9}}\cdot \pi \cdot r^{2}+{\frac {12\pi }{r}}}
f ( x ) = 1 x {\displaystyle f(x)={\frac {1}{x}}}
f ( x ) = x {\displaystyle f(x)={\sqrt {x}}}
f ( x ) = 1 20 − x ⋅ 2 x − 30 + 1 x 2 − 10000 {\displaystyle f(x)={\frac {1}{20-x}}\cdot {\sqrt {2x-30}}+{\frac {1}{x^{2}-10000}}}
1 6 − 2 3 ( 1 4 x − 1 2 x − 1 x ) = 1 {\displaystyle {\frac {1}{6}}-{\frac {2}{3}}\left({\frac {1}{4x}}-{\frac {1}{2x}}-{\frac {1}{x}}\right)=1}
1 1 a + 1 a = a b b + a {\displaystyle {\frac {1}{{\frac {1}{a}}+{\frac {1}{a}}}}={\frac {ab}{b+a}}}
