limit as x approaches 1 of \sqrt[x-1]{x}

Lösung

x \to 1 lim (x - 1 x)

e

Dezimale

2.71828 \dots

Schritte zur Lösung

x \to 1 lim (x - 1 x)

Wende Exponentenregel an

= x \to 1 lim (e^{\frac{1}{x - 1} l n (x)})

Vereinfache

e^{\frac{1}{x - 1} l n (x)} : x^{\frac{1}{x - 1}}

= x \to 1 lim (x^{\frac{1}{x - 1}})

Wende Exponentenregel an

= x \to 1 lim (e^{\frac{1}{x - 1} l n (x)})

Wende die Kettenregel für Grenzen an:

e

= e

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

\int \frac{sin ( 5 x )}{1 - cos ( 5 x )} d x

\frac{d y}{( 1 + 4 y ^{2} )} = - \frac{x}{( 1 + x ^{4} )} d x

d er i v a t i v e 6 x^{\frac{3}{2}}

x \to \infty lim (0.9 9^{x})