First slide

Continuity

Question

If $f (x) = \underset{x \to \infty}{L t} {(\sin x)}^{2 n},$ then f(x) is

Moderate

A

discontinuous at $x = \frac{π}{2}$
B

continuous at $x = \frac{π}{2}$
C

discontinuous at $x = - π / 2$
D

discontinuous at infinite number of points

Solution

$I f f (x) = \underset{x \to \infty}{L t} {(\sin^{2} x)}^{n} = \{\begin{matrix} 1, i f x = (2 n + 1) \frac{π}{2}, & \forall n \in Z \\ 0, i f x \neq (2 n + 1) \frac{π}{2}, & \forall n \in z \end{matrix} \begin{matrix} \end{matrix}$

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