Determine the right-hand limit of |x|/x as x approaches 0.

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Multiple Choice

Determine the right-hand limit of |x|/x as x approaches 0.

Explanation:
When approaching from the right, x is positive and near zero, so |x| equals x. The ratio |x|/x becomes x/x, which is 1 for all such x. Therefore the right-hand limit is 1. The other values don’t fit because from the right the expression is not approaching 0 or infinity; it stays constant at 1. (Note that from the left, the value would be -1, so the two-sided limit does not exist.)

When approaching from the right, x is positive and near zero, so |x| equals x. The ratio |x|/x becomes x/x, which is 1 for all such x. Therefore the right-hand limit is 1. The other values don’t fit because from the right the expression is not approaching 0 or infinity; it stays constant at 1. (Note that from the left, the value would be -1, so the two-sided limit does not exist.)

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