Question

The function f defined by f(x) =$\underset{n \rightarrow \infty}{Lim}$is

• A. Everywhere continuous
• B. Discontinuous at all integer values of x
• C. Continuous at x = 0
• D. None of these

Answer 1

Answer: (B)

Discontinuous at all integer values of x

Answer 2

sin πx > 0 (1^st & 2^nd quadrant)

⇒ 2nπ < πx <2nπ + π ⇒ 2n < x < 2n +1, n ∈ I sin πx < 0

(III & IV quadrant) 2nπ + π < πx < 2nπ + 2π

⇒ 2n +1 < x < 2n +2

f(x) =

=

Discontinuous at all integer.