limit as t approaches 0 of (3/(tsqrt(1+t)))-3/t

Lösung

t \to 0 lim ((\frac{3}{t 1 + t}) - \frac{3}{t})

- \frac{3}{2}

Dezimale

- 1.5

Schritte zur Lösung

t \to 0 lim (\frac{3}{t 1 + t} - \frac{3}{t})

Rationalisiere den Zähler

\frac{3}{t 1 + t} - \frac{3}{t} : - \frac{3}{( t + 1 + 1 ) t + 1}

= t \to 0 lim (- \frac{3}{( t + 1 + 1 ) t + 1})

Setze den Wert

t = 0

ein

= - \frac{3}{( 0 + 1 + 1 ) 0 + 1}

(0 + 1 + 1) 0 + 1 = 2

= - \frac{3}{2}

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