What is the limit as x approaches infinity of (arctan(4x))/8 ?

The limit as x approaches infinity of (arctan(4x))/8 is pi/(16)

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limit as x approaches infinity of (arctan(4x))/8

x \to \infty lim (\frac{arctan ( 4 x )}{8})

\frac{π}{16}

Decimal Notation

0.19634 \dots

Solution steps

x \to \infty lim (\frac{arctan ( 4 x )}{8})

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

= \frac{1}{8} \cdot x \to \infty lim (arctan (4 x))

Apply the Limit Chain Rule:

\frac{π}{2}

= \frac{1}{8} \cdot \frac{π}{2}

Simplify

\frac{1}{8} \cdot \frac{π}{2} : \frac{π}{16}

= \frac{π}{16}

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

h \to 0 lim (\frac{h}{e ^{h} - 1})

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

x \to 0 - lim ((1 - e^{x})^{2 x})

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

What is the limit as x approaches infinity of (arctan(4x))/8 ?
The limit as x approaches infinity of (arctan(4x))/8 is pi/(16)