Epsilon-delta Challenge

Calculus Level 1

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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