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Beliebt Rechnen >

limit as t approaches 0 of (8^t-5^t)/t

Lösung

t \to 0 lim (\frac{8 ^{t} - 5 ^{t}}{t})

Lösung

3 ln (2) - ln (5)

+1

Dezimale

0.47000 \dots

Schritte zur Lösung

t \to 0 lim (\frac{8 ^{t} - 5 ^{t}}{t})

Wende das L'Hopital Theorem an

= t \to 0 lim (\frac{3 ln ( 2 ) \cdot 8 ^{t} - 5 ^{t} ln ( 5 )}{1})

Setze den Wert

t = 0

ein

= \frac{3 ln ( 2 ) \cdot 8 ^{0} - 5 ^{0} ln ( 5 )}{1}

Vereinfache

\frac{3 ln ( 2 ) \cdot 8 ^{0} - 5 ^{0} ln ( 5 )}{1} : 3 ln (2) - ln (5)

= 3 ln (2) - ln (5)

Graph

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