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A function has a removable discontinuity at a point when

  • A.the two one-sided limits exist and differ from one another
  • B.the function grows without bound as the point is approached
  • C.the function oscillates ever faster near the point
  • D.the limit exists there but differs from the value assigned

Answer: D

A removable discontinuity is one that redefining a single value repairs: the limit \( \lim_{x \to a} f(x) \) exists, but \( f(a) \) is either absent or set to something else. Unequal one-sided limits give a jump, unbounded growth an infinite discontinuity, and faster oscillation an essential one, and none of those three can be repaired by changing one value

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