limit as t approaches infinity of (ln(3t))/(t^2)

Lösung

t \to \infty lim (\frac{ln ( 3 t )}{t ^{2}})

0

Schritte zur Lösung

t \to \infty lim (\frac{ln ( 3 t )}{t ^{2}})

Wende das L'Hopital Theorem an

= t \to \infty lim (\frac{\frac{1}{t}}{2 t})

Vereinfache

\frac{\frac{1}{t}}{2 t} : \frac{1}{2 t ^{2}}

= t \to \infty lim (\frac{1}{2 t ^{2}})

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

= \frac{1}{2} \cdot t \to \infty lim (\frac{1}{t ^{2}})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

mit Einschränkung des unbestimmten Ausdrucks

= \frac{1}{2} \cdot \frac{lim _{t \to \infty} ( 1 )}{lim _{t \to \infty} ( t ^{2} )}

t \to \infty lim (1) = 1

t \to \infty lim (t^{2}) = \infty

= \frac{1}{2} \cdot \frac{1}{\infty}

Vereinfache

\frac{1}{2} \cdot \frac{1}{\infty} : 0

= 0

x \to 1 lim (x^{2} + 2 x + 5)

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

x \to - 5 lim (- 35 + 3 x + 2 x^{2})

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

x \to \infty lim (x^{e})