Evaluate the Limit limit as x approaches 0 of 2/x

Problem

(lim_x→0)(2/x)

Solution

1. Analyze the behavior of the function as x approaches 0 from the right. As x takes on very small positive values, the fraction 2/x becomes a very large positive number.

(lim_x→0)(2/x)=∞

2. Analyze the behavior of the function as x approaches 0 from the left. As x takes on very small negative values, the fraction 2/x becomes a very large negative number.

(lim_x→0)(2/x)=−∞

3. Compare the one-sided limits. Since the limit from the right and the limit from the left are not equal, the two-sided limit does not exist.

∞≠−∞

Final Answer

(lim_x→0)(2/x)=Does Not Exist

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