de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

limit as x approaches infinity of 8xe^{1/x}-8x

Lösung

x \to \infty lim (8 x e^{\frac{1}{x}} - 8 x)

Lösung

8

Schritte zur Lösung

x \to \infty lim (8 x e^{\frac{1}{x}} - 8 x)

Wende die folgende algebraische Eigenschaft an

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

8 x e^{\frac{1}{x}} - 8 x = x (8 e^{\frac{1}{x}} - 8)

= x \to \infty lim (x (8 e^{\frac{1}{x}} - 8))

Umformung für L'Hopital

= x \to \infty lim (\frac{- 8 + 8 e ^{\frac{1}{x}}}{\frac{1}{x}})

Wende das L'Hopital Theorem an

= x \to \infty lim \frac{- \frac{8 e ^{\frac{1}{x}}}{x ^{2}}}{- \frac{1}{x ^{2}}}

Vereinfache

\frac{- \frac{8 e ^{\frac{1}{x}}}{x ^{2}}}{- \frac{1}{x ^{2}}} : 8 e^{\frac{1}{x}}

= x \to \infty lim (8 e^{\frac{1}{x}})

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

= 8 \cdot x \to \infty lim (e^{\frac{1}{x}})

Wende die Kettenregel für Grenzen an:

1

= 8 \cdot 1

Vereinfache

= 8

Graph

Beliebte Beispiele

integral of (x^2+x)^7(2x+1)

\int (x^{2} + x)^{7} (2 x + 1) d x

integral from 0 to 1 of e^x-e^{-x}

\int_{0}^{1} e^{x} - e^{- x} d x

tangent f(x)=e^x(9-3x+2x^2),\at x=0

t an g e n t f (x) = e^{x} (9 - 3 x + 2 x^{2}), at x = 0

integral of (e^{4x})/(1+e^x)

\int \frac{e ^{4 x}}{1 + e ^{x}} d x

integral of t(1-ln^2(t))

\int t (1 - ln^{2} (t)) d t