Evaluate the Limit limit as x approaches 5 of 2/(x-5)

Problem

(lim_x→5)(2/(x−5))

Solution

1. Identify the type of limit by substituting the value x=5 into the expression.

2. Observe that the numerator is a constant 2 and the denominator approaches 0

3. Analyze the one-sided limit as x approaches 5 from the right (x→5. In this case, x−5 is a very small positive number, so the fraction 2/(x−5) approaches +∞

4. Analyze the one-sided limit as x approaches 5 from the left (x→5. In this case, x−5 is a very small negative number, so the fraction 2/(x−5) approaches −∞

5. Conclude that since the left-hand limit and the right-hand limit are not equal, the two-sided limit does not exist.

Final Answer

(lim_x→5)(2/(x−5))=Does Not Exist

Want more problems? Check here!