limit as x approaches infinity of (sin(5x))/(5x)

Lösung

x \to \infty lim (\frac{sin ( 5 x )}{5 x})

0

Schritte zur Lösung

x \to \infty lim (\frac{sin ( 5 x )}{5 x})

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

= \frac{1}{5} \cdot x \to \infty lim (\frac{sin ( 5 x )}{x})

Wende den Einschnürungssatz an:

0

= \frac{1}{5} \cdot 0

Vereinfache

= 0

x \to 0 lim (\frac{1}{4})

x \to 0 lim (\frac{1}{- x})

x \to \frac{π}{2} lim (7 cos (- 5 x) sec (- 7 x))

x \to \infty lim (\frac{( 10 - 6 x ^{2} )}{5 + 3 e ^{x}})

x \to 0 lim (\frac{arccot ( x )}{x})