h ( x ) = H ′ ( x ) = H ′ ( H ( a ) + ∫ a x h ( t ) d t ) = H ′ ( a ) + H ′ ( ∫ a x h ( t ) d t ) = H ′ ( ∫ a x h ( t ) d t ) = H ′ ( H ( x ) − H ( a ) ) {\displaystyle h(x)=H'(x)=H'\left(H(a)+\int _{a}^{x}h(t)\,dt\right)=H'(a)+H'\left(\int _{a}^{x}h(t)\,dt\right)=H'\left(\int _{a}^{x}h(t)\,dt\right)=H'\left(H(x)-H(a)\right)}
h ( x ) = H ′ ( x ) = ( H ( a ) + ∫ a x h ( t ) d t ) ′ = H ′ ( a ) + ( ∫ a x h ( t ) d t ) ′ = 0 + ( ∫ a x h ( t ) d t ) ′ = ( H ( x ) − H ( a ) ) ′ = H ′ ( x ) − H ′ ( a ) {\displaystyle h(x)=H'(x)=\left(H(a)+\int _{a}^{x}h(t)\,dt\right)'=H'(a)+\left(\int _{a}^{x}h(t)\,dt\right)'=0+\left(\int _{a}^{x}h(t)\,dt\right)'=\left(H(x)-H(a)\right)'=H'(x)-H'(a)}
AKreis
m3
2 , 5 {\displaystyle 2,5}
2.5 {\displaystyle 2.5}
2 , 5 {\displaystyle 2{,}5}
Text ∫ a b {\displaystyle \int _{a}^{b}} Text
Text ∫ a b {\textstyle \int _{a}^{b}} Text
x = ^ {\displaystyle x{\widehat {=}}} Test
1 Löse folgendes Gleichungssystem mit dem Einsetzungsverfahren: I 7 x − 2 y = 48 II 3 x + 11 y = 11 {\displaystyle {\begin{array}{crrrrr}\\{\text{I}}\quad &7x&-&2y&=&48\\{\text{II}}\quad &3x&+&11y&=&11\end{array}}}
2 Beispielfrage
A Kreis = π ⋅ r 2 = π ⋅ 42 2 = π ⋅ 1.764 2 ≈ 5.541 , 7 {\displaystyle {\begin{aligned}A_{\text{Kreis}}&=\pi \cdot r^{2}\\&=\pi \cdot 42^{2}\\&=\pi \cdot 1.764^{2}\\&\approx 5.541{,}7\end{aligned}}}
I 7 x − 2 y = 48 II 3 x + 11 y = 11 {\displaystyle {\begin{array}{crrrrr}\\{\text{I}}\quad &7x&-&2y&=&48\\{\text{II}}\quad &3x&+&11y&=&11\end{array}}}
x 2 + 24 = 42 − 0 ∣ Termumformung ⇔ x 2 + 24 = 42 ∣ − 24 ⇔ x 2 = 18 ∣ ± ⇔ x = ± 18 {\displaystyle {\begin{aligned}&&x^{2}+24&=42-0&&\mid {\text{Termumformung}}\\\Leftrightarrow &&x^{2}+24&=42&&\mid -24\\\Leftrightarrow &&x^{2}&=18&&\mid \pm {\sqrt {}}\\\Leftrightarrow &&x&=\pm {\sqrt {18}}\end{aligned}}}