Evaluate the Limit limit as x approaches 0 of 1/x

Problem

(lim_x→0)(1/x)

Solution

1. Analyze the behavior of the function as x approaches 0 from the right side (x→0. As x becomes a very small positive number, the value of 1/x increases without bound toward positive infinity.

(lim_x→0)(1/x)=∞

2. Analyze the behavior of the function as x approaches 0 from the left side (x→0. As x becomes a very small negative number, the value of 1/x decreases without bound toward negative infinity.

(lim_x→0)(1/x)=−∞

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

∞≠−∞

Final Answer

(lim_x→0)(1/x)=Does Not Exist

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