In Example 5, we found the curvature of the helix r(t) = (a cos t)i + (a sin t)j + btk (a, b ≥ 0) to be k = a/(a² + b²). What is the largest value k can have for a given value of b? Give reasons for your answer.

In Figure 13.22

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EXAMPLE 5 Find the curvature for the helix (Figure 13.22) a, b = 0, r(t) = (a cos t)i + (a sin t)j + btk, a² + b² = 0.