limit as x approaches 1 of (x^8-1)/(x-1)

Lösung

x \to 1 lim (\frac{x ^{8} - 1}{x - 1})

8

Schritte zur Lösung

x \to 1 lim (\frac{x ^{8} - 1}{x - 1})

Vereinfache

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

= x \to 1 lim ((x^{2} + 2 x + 1) (x^{2} - 2 x + 1) (x^{2} + 1) (x + 1))

Setze den Wert

x = 1

ein

= (1^{2} + 2 \cdot 1 + 1) (1^{2} - 2 \cdot 1 + 1) (1^{2} + 1) (1 + 1)

Vereinfache

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

= 8

n = 1 \sum \infty \frac{( 3 ^{n - 1} )}{9 ^{n}}

\int_{1}^{2} 2 x x^{2} + 1 d x

n = 3 \sum \infty \frac{1}{3 ^{n}}

d er i v a t i v e (\frac{1}{y ^{2}} - \frac{7}{y ^{4}}) (y + 3 y^{3})

\int \frac{1}{e ^{u}} d u