# Epsilon-delta Challenge

**Calculus**Level 2

For the function \(f(x) = 3x^2 + 2x + 1,\) Alice wants Bob to show that \(\displaystyle \lim_{x \rightarrow 2} f(x) = 17\) using the \(\varepsilon\)-\(\delta\) definition of a limit.

Alice says, "I bet you can't choose a real number \(\delta\) so that for all \(x\) in \((2 - \delta, 2 + \delta)\), we'll have that \(\left|f(x) - 17\right| < 0.5\)."

Which of the following four choices is the largest \(\delta\) that Bob could give so that he completes Alice's challenge?

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