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Límite de la función Abs(-pi/2+atan(n-x))

Ha introducido [src]

     |-pi               |
 lim |---- + atan(n - x)|
x->oo| 2                |

\lim_{x \to \infty} \left|{\operatorname{atan}{\left(n - x \right)} + \frac{\left(-1\right) \pi}{2}}\right|

Limit(Abs((-pi)/2 + atan(n - x)), x, oo, dir='-')

Método de l'Hopital

En el caso de esta función, no tiene sentido aplicar el Método de l'Hopital, ya que no existe la indeterminación tipo 0/0 or oo/oo

Otros límites con x→0, -oo, +oo, 1

\lim_{x \to \infty} \left|{\operatorname{atan}{\left(n - x \right)} + \frac{\left(-1\right) \pi}{2}}\right| = \pi

\lim_{x \to 0^-} \left|{\operatorname{atan}{\left(n - x \right)} + \frac{\left(-1\right) \pi}{2}}\right| = \frac{\left(2 \operatorname{atan}{\left(n \right)} - \pi\right) \operatorname{sign}{\left(\operatorname{atan}{\left(n \right)} - \frac{\pi}{2} \right)}}{2}

\lim_{x \to 0^+} \left|{\operatorname{atan}{\left(n - x \right)} + \frac{\left(-1\right) \pi}{2}}\right| = \frac{\left(\pi - 2 \operatorname{atan}{\left(n \right)}\right) \operatorname{sign}{\left(- \operatorname{atan}{\left(n \right)} + \frac{\pi}{2} \right)}}{2}

\lim_{x \to 1^-} \left|{\operatorname{atan}{\left(n - x \right)} + \frac{\left(-1\right) \pi}{2}}\right| = \frac{\left(2 \operatorname{atan}{\left(n - 1 \right)} - \pi\right) \operatorname{sign}{\left(\operatorname{atan}{\left(n - 1 \right)} - \frac{\pi}{2} \right)}}{2}

\lim_{x \to 1^+} \left|{\operatorname{atan}{\left(n - x \right)} + \frac{\left(-1\right) \pi}{2}}\right| = \frac{\left(\pi - 2 \operatorname{atan}{\left(n - 1 \right)}\right) \operatorname{sign}{\left(- \operatorname{atan}{\left(n - 1 \right)} + \frac{\pi}{2} \right)}}{2}

\lim_{x \to -\infty} \left|{\operatorname{atan}{\left(n - x \right)} + \frac{\left(-1\right) \pi}{2}}\right| = 0

Respuesta rápida [src]

pi

\pi

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