Word Count : 290

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### 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 whether the limit of the function exists and matches the ________ ________ _________ ______ _____ _________ ______ ________ ______ _______.
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