limit as x approaches-3+of (x^2+9)/(x+3)

Lösung

x \to - 3 + lim (\frac{x ^{2} + 9}{x + 3})

\infty

Schritte zur Lösung

x \to - 3 + lim (\frac{x ^{2} + 9}{x + 3})

\frac{x ^{2} + 9}{x + 3} = (x^{2} + 9) \frac{1}{x + 3}

= x \to - 3 + lim ((x^{2} + 9) \frac{1}{x + 3})

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 - 3 + lim (x^{2} + 9) \cdot x \to - 3 + lim (\frac{1}{x + 3})

x \to - 3 + lim (x^{2} + 9) = 18

x \to - 3 + lim (\frac{1}{x + 3}) = \infty

= 18 \cdot \infty

Wende die Unendlichkeitseigenschaft an:

c \cdot \infty = \infty

= \infty

x \to \infty lim (\frac{sin ( 5 x )}{5 x})

x \to 0 lim (\frac{1}{4})

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

x \to \frac{π}{2} lim (7 cos (- 5 x) sec (- 7 x))

x \to \infty lim (\frac{( 10 - 6 x ^{2} )}{5 + 3 e ^{x}})