limit as x approaches 0 of (sin(2x))/x+1

Lösung

x \to 0 lim (\frac{sin ( 2 x )}{x} + 1)

3

Schritte zur Lösung

x \to 0 lim (\frac{sin ( 2 x )}{x} + 1)

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

mit Einschränkung des unbestimmten Ausdrucks

= x \to 0 lim (\frac{sin ( 2 x )}{x}) + x \to 0 lim (1)

x \to 0 lim (\frac{sin ( 2 x )}{x}) = 2

x \to 0 lim (1) = 1

= 2 + 1

Vereinfache

= 3

x \to 0 + lim (x sin (\frac{1}{5 x}))

x \to 0 lim (\frac{3 x ^{3} + 8 - x ^{2} + 4}{x ^{2}})

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

x \to 0 lim ((\frac{a ^{x} + b ^{x}}{2})^{\frac{1}{x}})

x \to 0 + lim (2 x ln (x))