Evaluate the Limit limit as x approaches 4 of 1/(x-4)

Problem

(lim_x→4)(1/(x−4))

Solution

1. Identify the type of limit by substituting the value x=4 into the expression.

2. Observe that the numerator is a constant 1 and the denominator approaches 0 as x approaches 4

3. Analyze the behavior from the right side as x→4 The denominator x−4 is a small positive number, so the fraction 1/(x−4) approaches +∞

4. Analyze the behavior from the left side as x→4 The denominator x−4 is a small negative number, so the fraction 1/(x−4) approaches −∞

5. Conclude that since the one-sided limits are not equal and do not approach a finite value, the limit does not exist.

Final Answer

(lim_x→4)(1/(x−4))=Does Not Exist

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