limit as x approaches 0+of 7/x-3/(x^2)

Lösung

x \to 0 + lim (\frac{7}{x} - \frac{3}{x ^{2}})

- \infty

Schritte zur Lösung

x \to 0 + lim (\frac{7}{x} - \frac{3}{x ^{2}})

Multipliziere mit der Konjugation von

\frac{7}{x} - \frac{3}{x ^{2}} : \frac{\frac{49}{x ^{2}} - \frac{9}{x ^{4}}}{\frac{7}{x} + \frac{3}{x ^{2}}}

= x \to 0 + lim (\frac{\frac{49}{x ^{2}} - \frac{9}{x ^{4}}}{\frac{7}{x} + \frac{3}{x ^{2}}})

Vereinfache

\frac{\frac{49}{x ^{2}} - \frac{9}{x ^{4}}}{\frac{7}{x} + \frac{3}{x ^{2}}} : \frac{7 x - 3}{x ^{2}}

= x \to 0 + lim (\frac{7 x - 3}{x ^{2}})

\frac{7 x - 3}{x ^{2}} = (7 x - 3) \frac{1}{x ^{2}}

= x \to 0 + lim ((7 x - 3) \frac{1}{x ^{2}})

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

mit Einschränkung des unbestimmten Ausdrucks

= x \to 0 + lim (7 x - 3) \cdot x \to 0 + lim (\frac{1}{x ^{2}})

x \to 0 + lim (7 x - 3) = - 3

x \to 0 + lim (\frac{1}{x ^{2}}) = \infty

= (- 3) \cdot \infty

Wende die Unendlichkeitseigenschaft an:

- c \cdot \infty = - \infty

= - \infty

x \to 0 + lim ((x + cos (x))^{\frac{4}{x}})

x \to 0 lim (3^{x + 1} - 3)

x \to - \frac{π}{2} lim (- 5 x - \frac{π}{2})

x \to 3 lim (\frac{( x + 2 )}{x - 3})

n \to \infty lim ((\frac{3 ^{n} + 2}{3 ^{n} - 1})^{3^{n}})