limit as x approaches infinity of (arcsec(x))/(sqrt(x))

Lösung

x \to \infty lim (\frac{arcsec ( x )}{x})

0

Schritte zur Lösung

x \to \infty lim (\frac{arcsec ( x )}{x})

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} ( arcsec ( x ) )}{lim _{x \to \infty} ( x )}

x \to \infty lim (arcsec (x)) = \frac{π}{2}

x \to \infty lim (x) = \infty

= \frac{\frac{π}{2}}{\infty}

Wende die Unendlichkeitseigenschaft an:

\frac{c}{\infty} = 0

= 0

x \to 0 - lim (\frac{∣ x ∣}{- 2 x})

x \to 0 lim (ln (1 - x^{2}))

x \to 1 lim (\frac{x ^{\frac{1}{4}} - 1}{x ^{\frac{1}{3}} - 1})

x \to 1 lim ((2 - x)^{7 t a n (\frac{π}{2} x)})

x \to \infty lim (4 x^{2} - 7 x - 2 x)