erweitern-((x+h)^4)/(4h)

Lösung

erweitern

- \frac{( x + h ) ^{4}}{4 h}

- \frac{x ^{4}}{4 h} - x^{3} - \frac{3 x ^{2} h}{2} - x h^{2} - \frac{h ^{3}}{4}

Schritte zur Lösung

- \frac{( x + h ) ^{4}}{4 h}

(x + h)^{4} = x^{4} + 4 x^{3} h + 6 x^{2} h^{2} + 4 x h^{3} + h^{4}

= - \frac{x ^{4} + 4 x ^{3} h + 6 x ^{2} h ^{2} + 4 x h ^{3} + h ^{4}}{4 h}

Wende Bruchregel an:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{x ^{4} + 4 x ^{3} h + 6 x ^{2} h ^{2} + 4 x h ^{3} + h ^{4}}{4 h} = - (\frac{x ^{4}}{4 h}) - (\frac{4 x ^{3} h}{4 h}) - (\frac{6 x ^{2} h ^{2}}{4 h}) - (\frac{4 x h ^{3}}{4 h}) - (\frac{h ^{4}}{4 h})

= - (\frac{x ^{4}}{4 h}) - (\frac{4 x ^{3} h}{4 h}) - (\frac{6 x ^{2} h ^{2}}{4 h}) - (\frac{4 x h ^{3}}{4 h}) - (\frac{h ^{4}}{4 h})

Entferne die Klammern:

(a) = a

= - \frac{x ^{4}}{4 h} - \frac{4 x ^{3} h}{4 h} - \frac{6 x ^{2} h ^{2}}{4 h} - \frac{4 x h ^{3}}{4 h} - \frac{h ^{4}}{4 h}

\frac{4 x ^{3} h}{4 h} = x^{3}

\frac{6 x ^{2} h ^{2}}{4 h} = \frac{3 x ^{2} h}{2}

\frac{4 x h ^{3}}{4 h} = x h^{2}

\frac{h ^{4}}{4 h} = \frac{h ^{3}}{4}

= - \frac{x ^{4}}{4 h} - x^{3} - \frac{3 x ^{2} h}{2} - x h^{2} - \frac{h ^{3}}{4}

e x p an d - \frac{3 ( s + 3 )}{s ( s + 2 ) ( s - 1 )}

e x p an d \frac{5}{( 3 x - 2 ) ^{2}}

e x p an d \frac{( x - 4 ) ( x + 1 )}{x - 3}

e x p an d \frac{x ^{2} ( x + 1 )}{x + 2}

e x p an d \frac{( 1 )}{( ( s ) ( s ^{2} + s + 1 ) )}