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AP Calculus BC/Unit 1: Limits and Continuity
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Vertical Asymptote as an Infinite Limit

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Which statement best describes the relationship between the vertical asymptote on the graph of f(x)=tan⁡(x)f(x) = \tan(x) at x=π2x = \frac{\pi}{2} and the concept of an infinite limit?

A

tan⁡(x)\tan(x) exhibits a jump discontinuity at x=π2x = \frac{\pi}{2}, unrelated to infinite limits.

B

The vertical asymptote at x=π2x = \frac{\pi}{2} represents a point where tan⁡(x)\tan(x) changes sign abruptly.

C

The function tan⁡(x)\tan(x) becomes undefined at x=π2x = \frac{\pi}{2}, but does not approach infinity.

D

As xx approaches π2\frac{\pi}{2}, tan⁡(x)\tan(x) grows without bound, exemplifying an infinite limit.

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