limit as x approaches 0 of ((484+x)^{0.5}-22)/x

Lösung

x \to 0 lim (\frac{( 484 + x ) ^{0.5} - 22}{x})

\frac{1}{44}

Dezimale

0.02272 \dots

Schritte zur Lösung

x \to 0 lim (\frac{( 484 + x ) ^{0.5} - 22}{x})

Multipliziere mit der Konjugation von

(484 + x)^{0.5} - 22 : \frac{x}{( 484 + x ) ^{0.5} + 22}

= x \to 0 lim (\frac{\frac{x}{( 484 + x ) ^{0.5} + 22}}{x})

Vereinfache

\frac{\frac{x}{( 484 + x ) ^{0.5} + 22}}{x} : \frac{1}{( x + 484 ) ^{\frac{1}{2}} + 22}

= x \to 0 lim (\frac{1}{( x + 484 ) ^{\frac{1}{2}} + 22})

Setze den Wert

x = 0

ein

= \frac{1}{( 0 + 484 ) ^{\frac{1}{2}} + 22}

Vereinfache

\frac{1}{( 0 + 484 ) ^{\frac{1}{2}} + 22} : \frac{1}{44}

= \frac{1}{44}

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