erweitern (sqrt((x+h)^2+1)-sqrt(x^2+1))/h

Lösung

erweitern

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

\frac{x ^{2} + 2 x h + h ^{2} + 1}{h} - \frac{x ^{2} + 1}{h}

Schritte zur Lösung

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

Multipliziere aus

(x + h)^{2} + 1 : x^{2} + 2 x h + h^{2} + 1

= \frac{x ^{2} + 2 x h + h ^{2} + 1 - x ^{2} + 1}{h}

Wende Bruchregel an:

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

\frac{x ^{2} + 2 x h + h ^{2} + 1 - x ^{2} + 1}{h} = \frac{x ^{2} + 2 x h + h ^{2} + 1}{h} - \frac{x ^{2} + 1}{h}

= \frac{x ^{2} + 2 x h + h ^{2} + 1}{h} - \frac{x ^{2} + 1}{h}

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

e x p an d (2 n)!

e x p an d 3 (x - 2)^{2} + 3 (x - 4)^{2}

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

e x p an d (3 t - \frac{4}{p})^{5}