limit as x approaches-infinity of (sqrt(x^2+8x))/(8x+1)

Lösung

x \to - \infty lim (\frac{x ^{2} + 8 x}{8 x + 1})

- \frac{1}{8}

Dezimale

- 0.125

Schritte zur Lösung

x \to - \infty lim (\frac{x ^{2} + 8 x}{8 x + 1})

Teile durch den größten gemeinsamen Potenznenner:

\frac{- 1 + \frac{8}{x}}{8 + \frac{1}{x}}

= x \to - \infty lim \frac{- 1 + \frac{8}{x}}{8 + \frac{1}{x}}

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

= - x \to - \infty lim \frac{1 + \frac{8}{x}}{8 + \frac{1}{x}}

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

mit Einschränkung des unbestimmten Ausdrucks

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

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

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

= - \frac{1}{8}

d er i v a t i v e f (x) = 2000 (x^{2} + 5)^{\frac{1}{3}}

\int_{0}^{2} e^{- x^{2}} d x

\frac{d}{d x} (4 x^{3} - 10 x^{2})

(4 x^{2})^{^{'}}

\frac{\partial}{\partial x} (e^{- (x - y)^{2}})