limit as x approaches 0+of xln(sin(x))

Lösung

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

0

Schritte zur Lösung

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

Umformung für L'Hopital

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

Wende das L'Hopital Theorem an

= x \to 0 + lim (\frac{cot ( x )}{- \frac{1}{x ^{2}}})

Vereinfache

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

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

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

Umformung für L'Hopital

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

Wende das L'Hopital Theorem an

= - x \to 0 + lim (\frac{2 x}{sec ^{2} ( x )})

Setze den Wert

x = 0

ein

= - \frac{2 \cdot 0}{sec ^{2} ( 0 )}

Vereinfache

- \frac{2 \cdot 0}{sec ^{2} ( 0 )} : 0

= 0

\int \frac{1}{5 x - 2} d x

\frac{d r}{d θ} = 8 (cos (\frac{θ}{3}))^{3}

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

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

\int \frac{1}{3 x ^{2} + 4 x + 5} d x