What is the limit as x approaches 1 of (arctan(x)-pi/4)/(x-1) ?

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

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limit as x approaches 1 of (arctan(x)-pi/4)/(x-1)

x \to 1 lim (\frac{arctan ( x ) - \frac{π}{4}}{x - 1})

\frac{1}{2}

Decimal Notation

0.5

Solution steps

x \to 1 lim (\frac{arctan ( x ) - \frac{π}{4}}{x - 1})

Apply L'Hopital's Rule

: x \to 1 lim (\frac{\frac{1}{x ^{2} + 1}}{1})

= x \to 1 lim (\frac{\frac{1}{x ^{2} + 1}}{1})

Plug in the value

x = 1

= \frac{\frac{1}{1 ^{2} + 1}}{1}

Simplify

= \frac{1}{2}

\int_{- r}^{r} π (r^{2} - x^{2}) d x

f (x) = 7 e^{x^{2} - 5 x + 8}, at x = 0

(3 x^{2} - 6 x + 6) e^{- 8 x}

y \frac{d y}{d x} = (y^{2} - y) (2 x + 5)

a^{2} - y^{2}

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