What is the left-hand limit of 1/(x-1) as x approaches 1?

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Multiple Choice

What is the left-hand limit of 1/(x-1) as x approaches 1?

Explanation:
Understanding what happens as x gets very close to 1 from values less than 1 is key. Here the denominator x−1 is a tiny negative number, so 1/(x−1) becomes a very large negative value. As the gap to 1 closes from the left, the expression dives toward negative infinity. So the left-hand limit is −∞. This contrasts with approaching from the right, which would give +∞, and explains why the function has a vertical asymptote at x = 1.

Understanding what happens as x gets very close to 1 from values less than 1 is key. Here the denominator x−1 is a tiny negative number, so 1/(x−1) becomes a very large negative value. As the gap to 1 closes from the left, the expression dives toward negative infinity. So the left-hand limit is −∞. This contrasts with approaching from the right, which would give +∞, and explains why the function has a vertical asymptote at x = 1.

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