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Beliebt Rechnen >

limit as x approaches 0+of (x^2e^{1/x})/(1+x^2)

Lösung

x \to 0 + lim (\frac{x ^{2} e ^{\frac{1}{x}}}{1 + x ^{2}})

Lösung

\infty

Schritte zur Lösung

x \to 0 + lim (\frac{x ^{2} e ^{\frac{1}{x}}}{1 + x ^{2}})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

mit Einschränkung des unbestimmten Ausdrucks

= \frac{lim _{x \to 0 +} ( x ^{2} e ^{\frac{1}{x}} )}{lim _{x \to 0 +} ( 1 + x ^{2} )}

x \to 0 + lim (x^{2} e^{\frac{1}{x}}) = \infty

x \to 0 + lim (1 + x^{2}) = 1

= \frac{\infty}{1}

Wende die Unendlichkeitseigenschaft an:

\frac{\infty}{c} = \infty

= \infty

Graph

Beliebte Beispiele

y^'=sqrt((x+3)/(y+8))

y^{^{'}} = \frac{x + 3}{y + 8}

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d er i v a t i v e f (x) = x^{2} - 9 x + 118

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

integral of 3(3x+2)

\int 3 (3 x + 2) d x

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