limit as x approaches infinity of (ln(7e^{3x}+2x^5))/(4x+3)

Lösung

x \to \infty lim (\frac{ln ( 7 e ^{3 x} + 2 x ^{5} )}{4 x + 3})

\frac{3}{4}

Dezimale

0.75

Schritte zur Lösung

x \to \infty lim (\frac{ln ( 7 e ^{3 x} + 2 x ^{5} )}{4 x + 3})

Wende das L'Hopital Theorem an

= x \to \infty lim (\frac{\frac{21 e ^{3 x} + 10 x ^{4}}{7 e ^{3 x} + 2 x ^{5}}}{4})

Wende Bruchregel an:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= x \to \infty lim (\frac{21 e ^{3 x} + 10 x ^{4}}{4 ( 7 e ^{3 x} + 2 x ^{5} )})

Wende das L'Hopital Theorem an

= x \to \infty lim (\frac{63 e ^{3 x} + 40 x ^{3}}{4 ( 21 e ^{3 x} + 10 x ^{4} )})

Wende das L'Hopital Theorem an

= x \to \infty lim (\frac{189 e ^{3 x} + 120 x ^{2}}{4 ( 63 e ^{3 x} + 40 x ^{3} )})

Wende das L'Hopital Theorem an

= x \to \infty lim (\frac{567 e ^{3 x} + 240 x}{4 ( 189 e ^{3 x} + 120 x ^{2} )})

Wende das L'Hopital Theorem an

= x \to \infty lim (\frac{1701 e ^{3 x} + 240}{4 ( 567 e ^{3 x} + 240 x )})

Wende das L'Hopital Theorem an

= x \to \infty lim (\frac{5103 e ^{3 x}}{4 ( 1701 e ^{3 x} + 240 )})

Wende das L'Hopital Theorem an

= x \to \infty lim (\frac{15309 e ^{3 x}}{20412 e ^{3 x}})

\frac{15309 e ^{3 x}}{20412 e ^{3 x}} = \frac{3}{4}

= x \to \infty lim (\frac{3}{4})

x \to a lim c = c

= \frac{3}{4}

x \to - \infty lim (\frac{1}{1 x})

x \to 0 lim (\frac{1 - cos ^{2} ( x - 2 )}{3 x ^{2} - 12 x + 12})

x \to - \infty lim (1 - \frac{3}{x})

x \to p (x) lim (\frac{g ( x ) { x } - g ( x ) { p ( x ) }}{x - p ( x )})

x \to \infty lim (\frac{π}{2} arctan (x))