limit as h approaches 0 of ((1+h)^8-1)/h

Lösung

h \to 0 lim (\frac{( 1 + h ) ^{8} - 1}{h})

8

Schritte zur Lösung

h \to 0 lim (\frac{( 1 + h ) ^{8} - 1}{h})

Vereinfache

\frac{( 1 + h ) ^{8} - 1}{h} : (h^{2} + 2 h + 2 h + 2 + 2) (h^{2} + 2 h - 2 h + 2 - 2) (h^{2} + 2 h + 2) (h + 2)

= h \to 0 lim ((h^{2} + 2 h + 2 h + 2 + 2) (h^{2} + 2 h - 2 h + 2 - 2) (h^{2} + 2 h + 2) (h + 2))

Setze den Wert

h = 0

ein

= (0^{2} + 2 \cdot 0 + 2 \cdot 0 + 2 + 2) (0^{2} + 2 \cdot 0 - 2 \cdot 0 + 2 - 2) (0^{2} + 2 \cdot 0 + 2) (0 + 2)

Vereinfache

(0^{2} + 2 \cdot 0 + 2 \cdot 0 + 2 + 2) (0^{2} + 2 \cdot 0 - 2 \cdot 0 + 2 - 2) (0^{2} + 2 \cdot 0 + 2) (0 + 2) : 8

= 8

\int ln (2 x + 3) d x

\int \frac{5 - x ^{2}}{( x ^{2} + 9 ) ( 3 - x )} d x

in v erse l a pl a ce \frac{2}{( s + 1 ) ( s + 2 ) ^{2}}

\frac{d y}{d x} = - \frac{e ^{x} y ^{2}}{10}

\int 3 ln^{2} (x) d x