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Beliebt Rechnen >

limit as x approaches 0 of (a^{2x}-1)/x

Lösung

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

Lösung

2 ln (a)

Schritte zur Lösung

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

Wende das L'Hopital Theorem an

= x \to 0 lim (\frac{2 a ^{2 x} ln ( a )}{1})

Setze den Wert

x = 0

ein

= \frac{2 a ^{2 \cdot 0} ln ( a )}{1}

Vereinfache

= 2 ln (a)

Graph

Beliebte Beispiele

limit as x approaches 7 of 1/(x^2(x+7))

x \to 7 lim (\frac{1}{x ^{2} ( x + 7 )})

derivative of asqrt(cos(2x))

\frac{d}{d x} (a cos (2 x))

integral of x/(sqrt(x^2+8x))

\int \frac{x}{x ^{2} + 8 x} d x

t an g e n t y = a x^{3}

integral from 0 to 1 of (ln(t))/t

\int_{0}^{1} \frac{ln ( t )}{t} d t