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Beliebt Rechnen >

limit as x approaches 0 of ((5^x-3^x))/x

Lösung

x \to 0 lim (\frac{( 5 ^{x} - 3 ^{x} )}{x})

Lösung

ln (5) - ln (3)

+1

Dezimale

0.51082 \dots

Schritte zur Lösung

x \to 0 lim (\frac{5 ^{x} - 3 ^{x}}{x})

Wende das L'Hopital Theorem an

= x \to 0 lim (\frac{5 ^{x} ln ( 5 ) - 3 ^{x} ln ( 3 )}{1})

Setze den Wert

x = 0

ein

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

Vereinfache

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

= ln (5) - ln (3)

Graph

Beliebte Beispiele

derivative of (50x/(0.01x^2+1))

\frac{d}{d x} (\frac{50 x}{0.01 x ^{2} + 1})

integral of (x^2+1)^{-3/2}

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

derivative f(x)=x^4-4x^3

d er i v a t i v e f (x) = x^{4} - 4 x^{3}

integral of x*sqrt(1-x^4)

\int x \cdot 1 - x^{4} d x

sum from n=0 to infinity of (1/2)^{n+1}

n = 0 \sum \infty (\frac{1}{2})^{n + 1}