limit as x approaches infinity of (x^2-1)/(8x^2-5)

Lösung

x \to \infty lim (\frac{x ^{2} - 1}{8 x ^{2} - 5})

\frac{1}{8}

Dezimale

0.125

Schritte zur Lösung

x \to \infty lim (\frac{x ^{2} - 1}{8 x ^{2} - 5})

Teile durch den größten gemeinsamen Potenznenner:

\frac{1 - \frac{1}{x ^{2}}}{8 - \frac{5}{x ^{2}}}

= x \to \infty lim (\frac{1 - \frac{1}{x ^{2}}}{8 - \frac{5}{x ^{2}}})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

mit Einschränkung des unbestimmten Ausdrucks

= \frac{lim _{x \to \infty} ( 1 - \frac{1}{x ^{2}} )}{lim _{x \to \infty} ( 8 - \frac{5}{x ^{2}} )}

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

x \to \infty lim (8 - \frac{5}{x ^{2}}) = 8

= \frac{1}{8}

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