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Beliebt Rechnen >

limit as x approaches infinity of (sqrt(x))/(ln(x))

Lösung

x \to \infty lim (\frac{x}{ln ( x )})

Lösung

\infty

Schritte zur Lösung

x \to \infty lim (\frac{x}{ln ( x )})

Wende das L'Hopital Theorem an

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

Vereinfache

\frac{\frac{1}{2 x}}{\frac{1}{x}} : \frac{1}{2} x

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

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= \frac{1}{2} \cdot x \to \infty lim (x)

x \to a lim [f (x)]^{b} = [x \to a lim f (x)]^{b}

mit Einschränkung des unbestimmten Ausdrucks

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

Wende die allgemeine Grenze an:

x \to \infty lim (x) = \infty

= \frac{1}{2} \infty

Vereinfache

\frac{1}{2} \infty : \infty

= \infty

Graph

Beliebte Beispiele

derivative of (x/2+1^3)

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

integral of e^{6x}sin(x)

\int e^{6 x} sin (x) d x

derivative f(x)=1.5x^7-(x^4)/3+pix-ex^2+sqrt(2)

d er i v a t i v e f (x) = 1.5 x^{7} - \frac{x ^{4}}{3} + π x - e x^{2} + 2

integral from 0 to pi/4 of sin(x)

\int_{0}^{\frac{π}{4}} sin (x) d x

derivative (48)/((1-x)^4)

d er i v a t i v e \frac{48}{( 1 - x ) ^{4}}