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AP Calculus BC/Unit 1: Limits and Continuity
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Classifying a Discontinuity

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Which of the following statements is true about the function f defined by f(x)=sin⁡(x)−tan⁡(x)x−π2f(x) = \frac{\sin(x) - \tan(x)}{x - \frac{\pi}{2}}?

A

f(x) is discontinuous at all odd multiples of π/2

B

f(x) is continuous for all real values of x

C

f(x) has an essential (infinite) discontinuity at x = π/2

D

f(x) has a removable discontinuity at x = π/2

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