limit as x approaches 0 of (6^x-5^x)/x

Lösung

x \to 0 lim (\frac{6 ^{x} - 5 ^{x}}{x})

ln (6) - ln (5)

Dezimale

0.18232 \dots

Schritte zur Lösung

x \to 0 lim (\frac{6 ^{x} - 5 ^{x}}{x})

Wende das L'Hopital Theorem an

= x \to 0 lim (\frac{6 ^{x} ln ( 6 ) - 5 ^{x} ln ( 5 )}{1})

Setze den Wert

x = 0

ein

= \frac{6 ^{0} ln ( 6 ) - 5 ^{0} ln ( 5 )}{1}

Vereinfache

\frac{6 ^{0} ln ( 6 ) - 5 ^{0} ln ( 5 )}{1} : ln (6) - ln (5)

= ln (6) - ln (5)

d er i v a t i v e f (x) = \frac{x - 3}{x + 3}

\frac{\partial}{\partial y} (\frac{x}{5 + y})

x \to - 1 lim (x - 1)

\frac{d ^{2}}{d t ^{2}} x + 5 \frac{d}{d t} x + 2 x = 0

\frac{\partial}{\partial y} (ln (x^{3} + y^{2}) - ln (x y))