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Beliebt Rechnen >

limit as x approaches 0 of (7^{sin(x)}-1)/x

Lösung

x \to 0 lim (\frac{7 ^{s i n (x)} - 1}{x})

Lösung

ln (7)

+1

Dezimale

1.94591 \dots

Schritte zur Lösung

x \to 0 lim (\frac{7 ^{s i n (x)} - 1}{x})

Wende das L'Hopital Theorem an

= x \to 0 lim (\frac{ln ( 7 ) \cdot 7 ^{s i n (x)} cos ( x )}{1})

Setze den Wert

x = 0

ein

= \frac{ln ( 7 ) \cdot 7 ^{s i n (0)} cos ( 0 )}{1}

Vereinfache

\frac{ln ( 7 ) \cdot 7 ^{s i n (0)} cos ( 0 )}{1} : ln (7)

= ln (7)

Graph

Beliebte Beispiele

integral of 1/9 x^{-8/9}

\int \frac{1}{9} x^{- \frac{8}{9}} d x

(\partial)/(\partial x)(x^3e^ysin(x-y))

\frac{\partial}{\partial x} (x^{3} e^{y} sin (x - y))

tangent f(x)=x^2-3,(3,6)

t an g e n t f (x) = x^{2} - 3, (3, 6)

maclaurin (4x)/(x^2+2x-3)

ma c l a u r in \frac{4 x}{x ^{2} + 2 x - 3}

derivative of 1/(5-11e^x)

\frac{d}{d x} (\frac{1}{5 - 11 e ^{x}})