One Sided Piecewise Limit: Worked Example and Solution
A complete one-sided branch analysis example with method choice, derivation, verification, and a common wrong approach.
1 problem8 min estimated timeFoundational to intermediate progression
What is included
See a concise answer and full derivation for for \(f(x)=\begin{cases}x+2,&x<1\\4-x,&x\ge1\end{cases}\), evaluate the limit as \(x\to1^-\).
Skills assessed
- One-sided branch analysis
Prerequisites
- function notation
- algebraic factoring
Printable preview
- For , evaluate the limit as .
Complete worked solutions
Every problem has a source-matched answer and independently reviewed derivation.
01
Problem 1: For , evaluate the limit as .
Answer:
Why this method: One-sided branch analysis matches the mathematical structure before any algebraic cleanup.
- Select the branch determined by the direction of approach.
- Evaluate nearby behavior on that branch; the value assigned at the endpoint does not control the limit.
- The required approach gives .
Common errors
- Using the branch selected by the endpoint equality instead of the approach direction.