What is the limit lim x->0 |x|?

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Multiple Choice

What is the limit lim x->0 |x|?

Explanation:
Think of |x| as the distance from x to zero. As x goes toward zero from either side, that distance shrinks to zero, so |x| goes to 0. Since absolute value is always nonnegative and becomes arbitrarily small near zero, the limit is 0. The other options don’t fit: you can’t approach 1 or -1 because the distance to zero tends to zero, not to those values, and you can’t go to infinity because the values stay small as x approaches zero.

Think of |x| as the distance from x to zero. As x goes toward zero from either side, that distance shrinks to zero, so |x| goes to 0. Since absolute value is always nonnegative and becomes arbitrarily small near zero, the limit is 0. The other options don’t fit: you can’t approach 1 or -1 because the distance to zero tends to zero, not to those values, and you can’t go to infinity because the values stay small as x approaches zero.

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