limit as x approaches infinity of 13x(e^{1/x})-13x

Lösung

x \to \infty lim (13 x (e^{\frac{1}{x}}) - 13 x)

13

Schritte zur Lösung

x \to \infty lim (13 x e^{\frac{1}{x}} - 13 x)

Wende die folgende algebraische Eigenschaft an

: a + b = a (1 + \frac{b}{a})

13 x e^{\frac{1}{x}} - 13 x = x (13 e^{\frac{1}{x}} - 13)

= x \to \infty lim (x (13 e^{\frac{1}{x}} - 13))

Umformung für L'Hopital

= x \to \infty lim (\frac{- 13 + 13 e ^{\frac{1}{x}}}{\frac{1}{x}})

Wende das L'Hopital Theorem an

= x \to \infty lim \frac{- \frac{13 e ^{\frac{1}{x}}}{x ^{2}}}{- \frac{1}{x ^{2}}}

Vereinfache

\frac{- \frac{13 e ^{\frac{1}{x}}}{x ^{2}}}{- \frac{1}{x ^{2}}} : 13 e^{\frac{1}{x}}

= x \to \infty lim (13 e^{\frac{1}{x}})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 13 \cdot x \to \infty lim (e^{\frac{1}{x}})

Wende die Kettenregel für Grenzen an:

1

= 13 \cdot 1

Vereinfache

= 13

y^{^{'}} = 8 - \frac{y}{200} 4, y (0) = 50

x \to \frac{π}{4} lim (sin (2 x))

\int_{- 1}^{2} \frac{x ^{2}}{3} d x

\frac{d}{d x} (\frac{4 sin ( x )}{5 cos ( y )})

t an g e n t f (x) = 2 x^{2} - 5 x + 2, at x = a