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Beliebt Rechnen >

limit as (x,y) approaches (0,0) of (x^2+y^2)ln(x^2+y^2)

Lösung

(x, y) \to (0, 0) lim ((x^{2} + y^{2}) ln (x^{2} + y^{2}))

Lösung

0^{2} ln (0^{2} + 0^{2}) + 0^{2} ln (0^{2} + 0^{2})

Schritte zur Lösung

(x, y) \to (0, 0) lim ((x^{2} + y^{2}) ln (x^{2} + y^{2}))

Klammere

x^{2}

aus

x^{2} + y^{2}

aus

: x^{2} (1 + \frac{y ^{2}}{x ^{2}})

= (x, y) \to (0, 0) lim (x^{2} (1 + \frac{y ^{2}}{x ^{2}}) ln (x^{2} + y^{2}))

Vereinfache

x^{2} (1 + \frac{y ^{2}}{x ^{2}}) ln (x^{2} + y^{2}) : x^{2} ln (x^{2} + y^{2}) + y^{2} ln (x^{2} + y^{2})

= (x, y) \to (0, 0) lim (x^{2} ln (x^{2} + y^{2}) + y^{2} ln (x^{2} + y^{2}))

Setze den Wert

(x, y) = (0, 0)

ein

= 0^{2} ln (0^{2} + 0^{2}) + 0^{2} ln (0^{2} + 0^{2})

Beliebte Beispiele

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s l o p e y = 4 x - x^{2}

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

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\int \frac{u}{u ^{2} + 1} d u

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x \to 0 lim (\frac{ln ( \frac{1 + x}{1 - x} ) - 2 x}{x - sin ( x )})