Calculus (Limits)

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Let f be defined as follows, where a does not = 0,

f(x) = {(x^2 - 2a + a^2) / (x-a), if x does not = a
5, if x = a

Which of the following are true about f?
I. lim f(x) exists as x approaches a
II. f(a) exists
III. f(x) is continuous at x = a.

A. None
B. I, II, and III
C. I only
D. II only
E. I and II only.

From my own knowledge, I would say that it is D. II only. Since we do not know what is equal to, we cannot determine what the limits or continuity would be at a. Is this correct?

  • Calculus (Limits) -

    I assume you do not have a typo and it is not x^2-2ax+a^2

    That said, the function is undefined and also discontinuous as x = a is approached. However since a separate f(a) is given the function exists at x = a so I agree D

  • Calculus (Limits) -

    No, its not a typo, it is supposed to be x^2 - 2a + a^2. Thank you for the reassurance, I figured that this was the most logical choice!

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