Word Count : 290

---

### Problem 1: Function Continuity We are given a piecewise function \( f: \mathbb{R} \to \mathbb{R} \) defined as: \[ f(x) = \begin{cases} \frac{1}{6}(x+1)^3 & \text{if } x \neq 0 \\ \frac{5}{6} & \text{if } x = 0 \end{cases} \] To examine its continuity, we need to check ____ ___ _____ _________ ______ ________ __________ ________ _________.
_____ ____ _________ ______ ________.
____ _________ _________ ______ ________ __________.
_____ _________ ________ __________ ___ ____ ____ ___ ______ _______.
_________ _________ ______ __________ _____.
________ ___ ______ __________ _______ _____ _______.
_______ _____ ___ _______ _________ ________.
________ __________ _______ ______ _________.
________ _________ _____ _______ ____.
_______ ______ _________ _________ ________ _________ _______ ____ __________ __________ _________ _______.
________ ___ ____ ______ _____ ______ __________ ________.
________ ________ ________ ___ ________ ________ ____ _________ ______ ___.
_________ ______ ___ _____ _________.
___ ______ ___ ______ ____ _____ __________ ____ ___ _________ ____.
________ _____ __________ _______ _________ _______ ___ ________ ______ ___ ________ ________.
_______ _________ _______ _________ __________ ________.
___ _______ ___ _____ ________ ______ _________ ________ ____.
___ _____ ____ ____ ___ ______ _________ _________ _________ _____ ____ __________.
________ ______ _________ ______ ____ ____ _____ __________.
________ _____ __________ ______ ________ __________ _______ _________ _____ ___ ___.
_________ _______ _____ _______ _________ ___ __________ ______ _______ ______.
______ ___ __________ __________ _______.
_______ _________ __________ ________ ____.
_________ _______ __________ ________ ____ __________ ____ _______.
_____ ______ _________ _______ ____ ______ ____ ______ ______ __________ ______ _____.
_________ _______ ______ __________ __________.
________ ________ _______ ______ ____ __________ ___ ______ ______.
____ ___ _____ _________ ______ _______ ______ ___ __________ _________.
___ ______ _________ ________ ____ _______ ___ _________ _______ _____.
_______ _________ ________ ________ ______.
__________.
Get Full Answer on WhatsApp