What is the limit as x approaches infinity of pi/2 arctan(x) ?

The limit as x approaches infinity of pi/2 arctan(x) is (pi^2)/4

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limit as x approaches infinity of pi/2 arctan(x)

x \to \infty lim (\frac{π}{2} arctan (x))

\frac{π ^{2}}{4}

Decimal

2.46740 \dots

Solution steps

x \to \infty lim (\frac{π}{2} arctan (x))

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

= \frac{π}{2} \cdot x \to \infty lim (arctan (x))

Apply the common limit:

x \to \infty lim (arctan (x)) = \frac{π}{2}

= \frac{π}{2} \cdot \frac{π}{2}

Simplify

\frac{π}{2} \cdot \frac{π}{2} : \frac{π ^{2}}{4}

= \frac{π ^{2}}{4}

x \to \infty lim (\frac{x ^{3} + 2 x ^{2} + 3 x + 4}{4 x ^{2} + 3 x ^{2} + 2 x + 1})

x \to - \infty lim (5 - x^{2})

x \to 0 lim ((x) (ln (x^{4})))

x \to 2 + lim (x (2))

x \to 3 + lim (x - 3)

What is the limit as x approaches infinity of pi/2 arctan(x) ?
The limit as x approaches infinity of pi/2 arctan(x) is (pi^2)/4