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

Lösung

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

\frac{1}{2}

Dezimale

0.5

Schritte zur Lösung

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

Wende das L'Hopital Theorem an

= x \to \infty lim (\frac{2 x + 2 ^{x} ln ( 2 )}{2 ( x + 1 ) + ln ( 2 ) \cdot 2 ^{x + 1}})

Wende das L'Hopital Theorem an

= x \to \infty lim (\frac{2 + ln ^{2} ( 2 ) \cdot 2 ^{x}}{2 + ln ^{2} ( 2 ) \cdot 2 ^{x + 1}})

Wende das L'Hopital Theorem an

= x \to \infty lim (\frac{ln ^{3} ( 2 ) \cdot 2 ^{x}}{ln ^{3} ( 2 ) \cdot 2 ^{x + 1}})

\frac{ln ^{3} ( 2 ) \cdot 2 ^{x}}{ln ^{3} ( 2 ) \cdot 2 ^{x + 1}} = \frac{1}{2}

= x \to \infty lim (\frac{1}{2})

x \to a lim c = c

= \frac{1}{2}