limit as x approaches 0+of x^2cot(4x^2)

Lösung

x \to 0 + lim (x^{2} cot (4 x^{2}))

\frac{1}{4}

Dezimale

0.25

Schritte zur Lösung

x \to 0 + lim (x^{2} cot (4 x^{2}))

Umformung für L'Hopital

= x \to 0 + lim (\frac{x ^{2}}{\frac{1}{c o t ( 4 x ^{2} )}})

Wende das L'Hopital Theorem an

= x \to 0 + lim (\frac{2 x}{sec ^{2} ( 4 x ^{2} ) \cdot 8 x})

Vereinfache

\frac{2 x}{sec ^{2} ( 4 x ^{2} ) \cdot 8 x} : \frac{1}{4} cos^{2} (4 x^{2})

= x \to 0 + lim (\frac{1}{4} cos^{2} (4 x^{2}))

Setze den Wert

x = 0

ein

= \frac{1}{4} cos^{2} (4 \cdot 0^{2})

Vereinfache

\frac{1}{4} cos^{2} (4 \cdot 0^{2}) : \frac{1}{4}

= \frac{1}{4}

x \to 2 lim (3 x^{2} + 3 x + 1)

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

x \to 2 + lim (\frac{x ^{2} - 5 x + 6}{x ^{2} - 7 x + 12})

x \to 0 lim (cos (x) \cdot ln (x))

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