limit as x approaches infinity of e^{1/2-1/(x^2)}-1

Lösung

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

e - 1

Dezimale

0.64872 \dots

Schritte zur Lösung

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

Vereinfache

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

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

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

mit Einschränkung des unbestimmten Ausdrucks

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

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

x \to \infty lim (1) = 1

= e - 1

n = 1 \sum \infty 1 (\frac{1}{6})^{n}

n = 1 \sum \infty n^{n} (x - 3)^{n}

\int_{0}^{\frac{π}{2}} \frac{cos ( θ )}{1 + sin ( θ )} d θ

n = 0 \sum \infty 2 (\frac{- 2}{3})^{n}

\frac{d y}{d x} = e^{- (x + y)}