limit as x approaches 0-of 1/(e^{1/x)-1}

Lösung

x \to 0 - lim (\frac{1}{e ^{\frac{1}{x}} - 1})

- 1

Schritte zur Lösung

x \to 0 - lim (\frac{1}{e ^{\frac{1}{x}} - 1})

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 0 -} ( 1 )}{lim _{x \to 0 -} ( e ^{\frac{1}{x}} - 1 )}

x \to 0 - lim (1) = 1

x \to 0 - lim (e^{\frac{1}{x}} - 1) = - 1

= \frac{1}{- 1}

Vereinfache

= - 1

d er i v a t i v e (x^{3} - x) (x^{2} + 2) (x^{2} + x - 1)

y^{^{''}} + 4 y^{^{'}} + 13 y = 0, y (0) = 2, y^{^{'}} (0) = - 2

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

\frac{d}{d x} (x^{2} - 1)

t an g e n t f (x) = (\frac{x + 1}{x - 3})^{2}, at x = 7