limit as x approaches infinity of (log_{4}(x))/(log_{9)(x)}

Lösung

x \to \infty lim (\frac{lo g _{4} ( x )}{lo g _{9} ( x )})

\frac{ln ( 3 )}{ln ( 2 )}

Dezimale

1.58496 \dots

Schritte zur Lösung

x \to \infty lim (\frac{lo g _{4} ( x )}{lo g _{9} ( x )})

Wende das L'Hopital Theorem an

= x \to \infty lim (\frac{\frac{1}{2 l n ( 2 ) x}}{\frac{1}{2 l n ( 3 ) x}})

\frac{\frac{1}{2 l n ( 2 ) x}}{\frac{1}{2 l n ( 3 ) x}} = \frac{ln ( 3 )}{ln ( 2 )}

= x \to \infty lim (\frac{ln ( 3 )}{ln ( 2 )})

x \to a lim c = c

= \frac{ln ( 3 )}{ln ( 2 )}

\int_{1}^{5} x - 1 d x

\int \frac{3}{7} x^{- \frac{1}{7}} d x

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

k = 0 \sum \infty k! 2^{k} x^{k}

t an g e n t f (x) = - 3 cos (x), at x = \frac{3}{4} π