Mathematics · JEE | CONTINUITY AND DIFFERENTIABILITY

Consider the following statements regarding continuity of functions: (A) If a function \( f \) is continuous at \( x = c \), then \( \lim_{x \to c} f(x) \) exists and equals \( f(c) \). (B) Every polynomial function is continuous at every real number. (C) The greatest integer function \( f(x) = [x] \) is continuous at all integer points. (D) If \( f \) and \( g \) are continuous at \( x = c \), then \( f + g \) is continuous at \( x = c \). Which of the above statements are correct?

1. A
   (A), (B) and (D) only
2. B
   and (C) only
3. C
   (B), (C) and (D) only
4. D
   (A), (B), (C) and (D)