What is the limit as x approaches infinity of arctan((x+1)/(x+2)) ?

The limit as x approaches infinity of arctan((x+1)/(x+2)) is pi/4

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limit as x approaches infinity of arctan((x+1)/(x+2))

x \to \infty lim (arctan (\frac{x + 1}{x + 2}))

\frac{π}{4}

Decimal

0.78539 \dots

Solution steps

x \to \infty lim (arctan (\frac{x + 1}{x + 2}))

Apply the Limit Chain Rule:

\frac{π}{4}

= \frac{π}{4}

What is the limit as x approaches infinity of arctan((x+1)/(x+2)) ?
The limit as x approaches infinity of arctan((x+1)/(x+2)) is pi/4