What is the limit as t approaches infinity of (ln(3t))/(t^2) ?

The limit as t approaches infinity of (ln(3t))/(t^2) is 0

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

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

0

Solution steps

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

Apply L'Hopital's Rule

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

Simplify

\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

With the exception of indeterminate form

= \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}

Simplify

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

= 0

What is the limit as t approaches infinity of (ln(3t))/(t^2) ?
The limit as t approaches infinity of (ln(3t))/(t^2) is 0