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Beliebt Rechnen >

limit as x approaches infinity of xsin((2pi)/x)

Lösung

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

Lösung

2 π

+1

Dezimale

6.28318 \dots

Schritte zur Lösung

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

Umformung für L'Hopital

= x \to \infty lim (\frac{sin ( \frac{2 π}{x} )}{\frac{1}{x}})

Wende das L'Hopital Theorem an

= x \to \infty lim \frac{- \frac{2 π c o s ( \frac{2 π}{x} )}{x ^{2}}}{- \frac{1}{x ^{2}}}

Vereinfache

\frac{- \frac{2 π c o s ( \frac{2 π}{x} )}{x ^{2}}}{- \frac{1}{x ^{2}}} : 2 π cos (\frac{2 π}{x})

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

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

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

Wende die Kettenregel für Grenzen an:

1

= 2 π 1

Vereinfache

= 2 π

Graph

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