1965 AHSME Problem 23

If we write |x^2 - 4| < N for all x such that |x - 2| < 0.01, the smallest value we can use for N is:

\textbf{(A)}\ .0301 \qquad \textbf{(B) }\ .0349 \qquad \textbf{(C) }\ .0399 \qquad \textbf{(D) }\ .0401 \qquad \textbf{(E) }\ .0499\qquad

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.