Word Count : 248

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To examine the continuity of the function: \[ f(x) = \begin{cases} \frac{1}{6} (x+1)^3, & x \neq 0 \\ \frac{5}{6}, & x = 0 \end{cases} \] ### Step 1: Check Continuity at \( x = 0 \) A function is continuous at \( x = 0 \) if: \[ \lim_{x _______ _____ ____ ___ _____.
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