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

Problem

(lim_x→−1)(1/(x+1))

Solution

1. Analyze the behavior of the function as x approaches −1 by substituting the value into the expression.

2. Observe that the denominator x+1 approaches 0 while the numerator remains a constant 1 which indicates a vertical asymptote.

3. Evaluate the one-sided limit from the right (x→−1, where x+1 is a small positive number, resulting in ∞

4. Evaluate the one-sided limit from the left (x→−1, where x+1 is a small negative number, resulting in −∞

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

Final Answer

(lim_x→−1)(1/(x+1))=Does Not Exist

Want more problems? Check here!