limit as t approaches 0 of (7^t-6^t)/t

Lösung

t \to 0 lim (\frac{7 ^{t} - 6 ^{t}}{t})

ln (7) - ln (6)

Dezimale

0.15415 \dots

Schritte zur Lösung

t \to 0 lim (\frac{7 ^{t} - 6 ^{t}}{t})

Wende das L'Hopital Theorem an

= t \to 0 lim (\frac{7 ^{t} ln ( 7 ) - 6 ^{t} ln ( 6 )}{1})

Setze den Wert

t = 0

ein

= \frac{7 ^{0} ln ( 7 ) - 6 ^{0} ln ( 6 )}{1}

Vereinfache

\frac{7 ^{0} ln ( 7 ) - 6 ^{0} ln ( 6 )}{1} : ln (7) - ln (6)

= ln (7) - ln (6)

x \to 0 lim ((4 x + 1)^{\frac{1}{x}})

b \to \infty lim (e^{- b})

x \to - \infty lim (7^{x})

x \to π lim (\frac{cos ( 2 x )}{x})

x \to \frac{2}{3} lim ((3 x^{2} - 2)^{5})