Mathematics · Real Analysis
Let f : ℝ2 → ℝ be a bounded function such that for each t ∈ ℝ, the functions gt and ht given by gt(y) = f(t, y) and ht(x) = f(x, t) are non-decreasing functions. Which of the following statements is necessarily true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1lim(x,y) → (+∞, -∞) f(x, y) exists
- 2lim(x,y) → (+∞, +∞) f(x, y) exists✓
- 3The number of discontinuities of f is at most countably infinite
- 4k(x) = f(x, x) is a non-decreasing function
Correct answer
lim(x,y) → (+∞, +∞) f(x, y) exists
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