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

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

Popular >

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

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

- \frac{π}{2}

Decimal

- 1.57079 \dots

Solution steps

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

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

With the exception of indeterminate form

= x \to - \infty lim (\frac{x}{x + 1}) \cdot x \to - \infty lim (arctan (x))

x \to - \infty lim (\frac{x}{x + 1}) = 1

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

= 1 \cdot (- \frac{π}{2})

Simplify

= - \frac{π}{2}

x \to 0 lim (\frac{( ln ( 2 e + x ) - ln ( 2 e ) )}{x})

x \to 2 lim (a x^{2} + 2 x)

x \to 1 lim ((3 x + 1) (x^{2} + 1))

x \to 0 lim (\frac{2 + \frac{1}{e ^{x}}}{1 + e ^{\frac{4}{x}}} + \frac{sin ( x )}{∣ x ∣})

x \to - \infty lim (\frac{5 x ^{6} - 1}{x ^{3} - 4})

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