limit as x approaches 0 of (cos(5x)tan(5x))/(3x)

Lösung

x \to 0 lim (\frac{cos ( 5 x ) tan ( 5 x )}{3 x})

\frac{5}{3}

Dezimale

1.66666 \dots

Schritte zur Lösung

x \to 0 lim (\frac{cos ( 5 x ) tan ( 5 x )}{3 x})

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{cos ( 5 x ) tan ( 5 x )}{x})

cos (5 x) tan (5 x) = sin (5 x)

= \frac{1}{3} \cdot x \to 0 lim (\frac{sin ( 5 x )}{x})

Wende das L'Hopital Theorem an

= \frac{1}{3} \cdot x \to 0 lim (\frac{cos ( 5 x ) \cdot 5}{1})

Setze den Wert

x = 0

ein

= \frac{1}{3} \cdot \frac{cos ( 5 \cdot 0 ) \cdot 5}{1}

Vereinfache

\frac{1}{3} \cdot \frac{cos ( 5 \cdot 0 ) \cdot 5}{1} : \frac{5}{3}

= \frac{5}{3}

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

\frac{\partial}{\partial x} (sin^{2} (a x))

\int 5 e^{5 x} sin (e^{5 x}) d x

\int 2 cos (x) d x

x \to 5 lim (cos (\frac{1}{x - 5}))