Theorems · Theorem · real analysis
tendsto_rpow_div
Filter.Tendsto (fun x => x ^ (1 / x)) Filter.atTop (nhds 1)
The function x ^ (1 / x) tends to 1 at +∞.
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- 0 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Filterproof · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- Filter.Tendstostatement and proof · cited by 3,814
- Nat.cast_oneproof · cited by 2,501
- Filter.atTopstatement and proof · cited by 2,405
- Nat.cast_zeroproof · cited by 1,870
- zero_ne_oneproof · cited by 90
- tendsto_rpow_div_mul_addproof · cited by 2
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