# 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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