What is the limit as x approaches 0 of arctan(x^2+1) ?

The limit as x approaches 0 of arctan(x^2+1) is pi/4

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limit as x approaches 0 of arctan(x^2+1)

x \to 0 lim (arctan (x^{2} + 1))

\frac{π}{4}

Decimal Notation

0.78539 \dots

Solution steps

x \to 0 lim (arctan (x^{2} + 1))

Plug in the value

x = 0

= arctan (0^{2} + 1)

Simplify

arctan (0^{2} + 1) : \frac{π}{4}

= \frac{π}{4}

\int_{0}^{1} \int_{0}^{2} x y e^{x y^{2}} d x d y

\int (e^{2 x} + 4)^{- 1} d x

\int_{l n (4)}^{l n (25)} e^{\frac{x}{2}} d x

x \to 0 lim (- \frac{5}{1 - 5 x})

\frac{d y}{d x} = \frac{1}{1 - x}, y (0) = 1

What is the limit as x approaches 0 of arctan(x^2+1) ?
The limit as x approaches 0 of arctan(x^2+1) is pi/4