limit as x approaches 0 of ((1-cos(x)))/(3x^2)

Lösung

x \to 0 lim (\frac{( 1 - cos ( x ) )}{3 x ^{2}})

\frac{1}{6}

Dezimale

0.16666 \dots

Schritte zur Lösung

x \to 0 lim (\frac{1 - cos ( x )}{3 x ^{2}})

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

= \frac{1}{3} \cdot x \to 0 lim (\frac{1 - cos ( x )}{x ^{2}})

Wende das L'Hopital Theorem an

= \frac{1}{3} \cdot x \to 0 lim (\frac{sin ( x )}{2 x})

Wende das L'Hopital Theorem an

= \frac{1}{3} \cdot x \to 0 lim (\frac{cos ( x )}{2})

Setze den Wert

x = 0

ein

= \frac{1}{3} \cdot \frac{cos ( 0 )}{2}

Vereinfache

\frac{1}{3} \cdot \frac{cos ( 0 )}{2} : \frac{1}{6}

= \frac{1}{6}

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

x \to - 1 + lim (2^{\frac{1}{x + 1}})

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

x \to \frac{1}{8} lim (\frac{1}{x} + x - 1)

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