limit as x approaches 0 of ((5^x-7^x))/x

Lösung

x \to 0 lim (\frac{( 5 ^{x} - 7 ^{x} )}{x})

ln (5) - ln (7)

Dezimale

- 0.33647 \dots

Schritte zur Lösung

x \to 0 lim (\frac{5 ^{x} - 7 ^{x}}{x})

Wende das L'Hopital Theorem an

= x \to 0 lim (\frac{5 ^{x} ln ( 5 ) - 7 ^{x} ln ( 7 )}{1})

Setze den Wert

x = 0

ein

= \frac{5 ^{0} ln ( 5 ) - 7 ^{0} ln ( 7 )}{1}

Vereinfache

\frac{5 ^{0} ln ( 5 ) - 7 ^{0} ln ( 7 )}{1} : ln (5) - ln (7)

= ln (5) - ln (7)

\frac{d}{d x} ((- 2 x^{3} + x^{2} - 2 x - 1) x^{3})

\frac{\partial}{\partial v} (u (v) (v)^{2} e^{v})

\frac{d}{d x} (\frac{d y}{d x}) = 0

d er i v a t i v e \frac{6 x ^{2} + 8 x + 2}{x}

\frac{\partial}{\partial x} (ln (\frac{y ^{9}}{x ^{7}}))