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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

\frac{π}{2}

Decimal Notation

1.57079 \dots

Solution steps

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

Apply the Limit Chain Rule:

\frac{π}{2}

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

Limit Chain Rule

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

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

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

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

Apply the common limit:

x \to \infty lim (x) = \infty

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

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

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

u \to \infty lim (arctan (u))

Apply the common limit:

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

= \frac{π}{2}

By the chain rule:

= \frac{π}{2}

= \frac{π}{2}

\frac{1}{cos ( 0.5 )}

arctan (0.767)

2.8 \cdot cos (6 0^{\circ})

arctan (\frac{- 3 3}{- 3})

sin^{2} (\frac{3 π}{4}) + cos^{2} (\frac{3 π}{4})

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