AI tutor
Welcome to Bytelearn!
Let’s check out your problem:
Solve:
Full solution
Q. Solve:
- Identify Function & Point: Identify the function and the point of interest. We are looking at the limit of the function as approaches .
- Substitute : Substitute directly into the function to check for any immediate simplification or issues. , which is undefined, indicating a potential issue at .
- Recognize Discontinuity: Recognize the type of discontinuity. Since direct substitution leads to a division by , this suggests a vertical asymptote at , meaning the limit might be infinite or does not exist.
- Analyze Behavior Approaching : Analyze the behavior of the function as approaches from both sides (left and right limits). As approaches from the left (), . As approaches from the right (), .
- Conclude Limit: Conclude the limit based on the behavior from both sides. Since the left-hand limit and the right-hand limit are not equal and both approach but with opposite signs, the overall limit does not exist.
