Find the One Sided Limits and the Regular Limit Given the Piecewise Function

TL;DR

This content explains how to find the limits of a piecewise function by considering different approaches from the left and right, and determines that the limit does not exist when the results are different.

Transcript

in this problem we have a piecewise function and we have to find three different limits let's go ahead and work through each one so first we'll find the limit of big f of x as x approaches one from the left so because we're approaching one from the left so here's a little picture here's one and then here's x because it's approaching from the left s... Read More

Key Insights

• ↔️ Limits of a piecewise function can be determined by considering approaching from the left and right.
• ☺️ Substituting x into the respective pieces of the function allows for easy evaluation of the limits.
• ⛔ If the limits from the left and right are different, the overall limit of the function does not exist.

Summary & Key Takeaways

• The content discusses finding the limit of a piecewise function as x approaches 1 from the left, resulting in a limit of 3.

• It then explores finding the limit as x approaches 1 from the right, giving a limit of 1.

• Finally, it concludes that because the limits from the left and right are different, the overall limit does not exist.