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 Notation

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}

\frac{\partial}{\partial x} (2 x^{2} + 3 y^{2})

\frac{d y}{d x} - 2 x y = 6 x

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

x \to π lim (\frac{sin ( x )}{x})

\frac{d}{d x} (1 - sin (x))

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