Question

If \(\lim\limits_{x \to a^-} f(x) = p\), \(\lim\limits_{x \to a^+} f(x) = m\), and \(f(a) = k\), then which one of the following is true?

• A. \(p - k = 0\) and \(m - k = 0\)
• B. \(p - k = 0\) and \(m - k \neq 0\)
• C. \(p - k \neq 0\) and \(m - k = 0\)
• D. \(p - m = 0\) and \(p - k \neq 0\)

Hint:

For continuity: limit from both sides must be equal and equal to \(f(a)\).

Answer 1

The Correct Option is D

From the given, \(\lim_{x \to a} f(x) = p = m\), so limit exists, but since \(f(a) \ne p\), function is not continuous. Hence, only limit exists and is not equal to value.