limit as x approaches infinity of 1/(arctan(sqrt(x)))

Lösung

x \to \infty lim (\frac{1}{arctan ( x )})

\frac{2}{π}

Dezimale

0.63661 \dots

Schritte zur Lösung

x \to \infty lim (\frac{1}{arctan ( 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} ( 1 )}{lim _{x \to \infty} ( arctan ( x ) )}

x \to \infty lim (1) = 1

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

= \frac{1}{\frac{π}{2}}

Vereinfache

= \frac{2}{π}

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

x \to a lim (\frac{x ^{5} - a ^{5}}{x ^{4} - a ^{4}})

x \to \infty lim (\frac{3 x - cos ( x )}{2 x + sin ( x )})

x \to \infty lim (\frac{4 x ^{2} + 5 x - 1}{x ^{2} - 7 x + 29})

x \to 1 lim (\frac{6 x + 1}{x - 1})