limit as x approaches 5+of x/(x^2-25)

Lösung

x \to 5 + lim (\frac{x}{x ^{2} - 25})

\infty

Schritte zur Lösung

x \to 5 + lim (\frac{x}{x ^{2} - 25})

\frac{x}{x ^{2} - 25} = x \frac{1}{x ^{2} - 25}

= x \to 5 + lim (x \frac{1}{x ^{2} - 25})

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 5 + lim (x) \cdot x \to 5 + lim (\frac{1}{x ^{2} - 25})

x \to 5 + lim (x) = 5

x \to 5 + lim (\frac{1}{x ^{2} - 25}) = \infty

= 5 \cdot \infty

Wende die Unendlichkeitseigenschaft an:

c \cdot \infty = \infty

= \infty

x \to 8 - lim (- \frac{7}{x ^{2} - 8 x})

x \to 0 lim (x ln ∣ 6 x ∣)

x \to 1 + lim ((x - 1) ln (x - 1))

x \to 0 lim (\frac{cos ( 3 x ) - cos ( 4 x )}{x ^{2}})

x \to a lim (\frac{1}{f ( x )})