Mathematics · Limits, Continuity and Differentiability

Let f : [0, ∞) → [0, ∞) be defined as f(x) = ∫0x [y] dy, where [y] is the greatest integer less than or equal to y. Which of the following is true?

Verified Solution4 OptionsUpdated: October 2026👁️1 View

1f is differentiable at every point in [0, ∞).
2f is continuous everywhere except at the integer points in [0, ∞).
3f is both continuous and differentiable except at the integer points in [0, ∞).
4f is continuous at every point in [0, ∞) and differentiable except at the integer points.✓

Correct answer

f is continuous at every point in [0, ∞) and differentiable except at the integer points.

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