Mathematics

Mathematics

Problem

The function hh satisfies lim⁡x→−1−h(x)=4\displaystyle \lim_{x\to -1^-}h(x)=4, lim⁡x→−1+h(x)=2\displaystyle \lim_{x\to -1^+}h(x)=2, and h(−1)=4h(-1)=4. Which of the following is correct? a) lim⁡x→−1h(x) exists and equals 4, and h is continuous at x=−1\displaystyle \lim_{x\to -1}h(x)\text{ exists and equals }4,\text{ and }h\text{ is continuous at }x=-1 b) lim⁡x→−1h(x) does not exist and h is discontinuous at x=−1\displaystyle \lim_{x\to -1}h(x)\text{ does not exist and }h\text{ is discontinuous at }x=-1 c) lim⁡x→−1h(x) exists and equals 2, but h is discontinuous at x=−1\displaystyle \lim_{x\to -1}h(x)\text{ exists and equals }2,\text{ but }h\text{ is discontinuous at }x=-1 d) lim⁡x→−1h(x) exists and equals 3, and h is discontinuous at x=−1\displaystyle \lim_{x\to -1}h(x)\text{ exists and equals }3,\text{ and }h\text{ is discontinuous at }x=-1

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