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Beliebt Rechnen >

limit as x approaches 0 of ((6^x-8^x))/x

Lösung

x \to 0 lim (\frac{( 6 ^{x} - 8 ^{x} )}{x})

Lösung

ln (6) - 3 ln (2)

+1

Dezimale

- 0.28768 \dots

Schritte zur Lösung

x \to 0 lim (\frac{6 ^{x} - 8 ^{x}}{x})

Wende das L'Hopital Theorem an

= x \to 0 lim (\frac{6 ^{x} ln ( 6 ) - 3 ln ( 2 ) \cdot 8 ^{x}}{1})

Setze den Wert

x = 0

ein

= \frac{6 ^{0} ln ( 6 ) - 3 ln ( 2 ) \cdot 8 ^{0}}{1}

Vereinfache

\frac{6 ^{0} ln ( 6 ) - 3 ln ( 2 ) \cdot 8 ^{0}}{1} : ln (6) - 3 ln (2)

= ln (6) - 3 ln (2)

Graph

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