limit as x approaches 1 of (sqrt(10-x)-sqrt(8+x))/(x^3-1)

Lösung

x \to 1 lim (\frac{10 - x - 8 + x}{x ^{3} - 1})

- \frac{1}{9}

Dezimale

- 0.11111 \dots

Schritte zur Lösung

x \to 1 lim (\frac{10 - x - 8 + x}{x ^{3} - 1})

Rationalisiere den Zähler

\frac{10 - x - 8 + x}{x ^{3} - 1} : - \frac{2}{( x ^{2} + x + 1 ) ( - x + 10 + x + 8 )}

= x \to 1 lim (- \frac{2}{( x ^{2} + x + 1 ) ( - x + 10 + x + 8 )})

Setze den Wert

x = 1

ein

= - \frac{2}{( 1 ^{2} + 1 + 1 ) ( - 1 + 10 + 1 + 8 )}

Vereinfache

- \frac{2}{( 1 ^{2} + 1 + 1 ) ( - 1 + 10 + 1 + 8 )} : - \frac{1}{9}

= - \frac{1}{9}

x \to - 3 + lim (- \frac{sin ( c - 3 x )}{e ^{5 x + 15} - 1})

x \to 0 + lim (\frac{e ^{x} - 1 - x}{x ^{2}})

t \to \infty lim (t e^{t})

x \to 0 lim (\frac{3}{2})

x \to 0 + lim (x^{9} (ln (x))^{2})