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

Lösung

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

\infty

Schritte zur Lösung

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

\frac{1}{x - 2} - \frac{1}{x - 2} = \frac{1}{x - 2} (1 - \frac{\frac{1}{x - 2}}{\frac{1}{x - 2}})

= x \to 2 + lim (\frac{1}{x - 2} (1 - \frac{\frac{1}{x - 2}}{\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 2 + lim (\frac{1}{x - 2}) \cdot x \to 2 + lim (1 - \frac{\frac{1}{x - 2}}{\frac{1}{x - 2}})

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

x \to 2 + lim (1 - \frac{\frac{1}{x - 2}}{\frac{1}{x - 2}}) = 1

= \infty \cdot 1

Wende die Unendlichkeitseigenschaft an:

c \cdot \infty = \infty

= \infty

\int \frac{1}{u ( 1 - u )} d u

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

\int (- 3 sec^{2} (x)) d x

\frac{\partial}{\partial y} (x 1 + y^{2})

\frac{\partial}{\partial y} (sin (x) cos (7 y))