limit as x approaches 0 of (sqrt(4+x)-sqrt(4-x))/(4x)

Lösung

x \to 0 lim (\frac{4 + x - 4 - x}{4 x})

\frac{1}{8}

Dezimale

0.125

Schritte zur Lösung

x \to 0 lim (\frac{4 + x - 4 - x}{4 x})

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

= \frac{1}{4} \cdot x \to 0 lim (\frac{4 + x - 4 - x}{x})

Rationalisiere den Zähler

\frac{4 + x - 4 - x}{x} : \frac{2}{x + 4 + - x + 4}

= \frac{1}{4} \cdot x \to 0 lim (\frac{2}{x + 4 + - x + 4})

Setze den Wert

x = 0

ein

= \frac{1}{4} \cdot \frac{2}{0 + 4 + - 0 + 4}

Vereinfache

\frac{1}{4} \cdot \frac{2}{0 + 4 + - 0 + 4} : \frac{1}{8}

= \frac{1}{8}

x \to - \frac{π}{2} lim (- tan (0.5 x))

\int_{0}^{\frac{π}{2}} x^{2} sin (x) d x

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

\frac{d}{d x} (ln (x^{3} - 2 x^{2}))

\int cos (0)