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AP Calculus BC/Unit 1: Limits and Continuity
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Limit and Removable Discontinuity

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Which of the following equations defines a function f(x)f(x) that has a removable discontinuity at x=−2x = -2 and for which lim⁡x→−2f(x)=1\lim_{x \to -2} f(x) = 1? (Do not use a calculator.)

A

2∗(x+4−2)x+2\frac{2*(\sqrt{x+4}-\sqrt{2})}{x+2}

B

2∗2⋅(x+4−2)x+2\frac{2*\sqrt{2}\cdot(\sqrt{x+4}-\sqrt{2})}{x+2}

C

2∗2⋅(x+4+2)x+2\frac{2*\sqrt{2}\cdot(\sqrt{x+4}+\sqrt{2})}{x+2}

D

x+4−2x+2\frac{\sqrt{x+4}-\sqrt{2}}{x+2}

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