Theorems · Theorem · real analysis
tendsto_exp_div_rpow_atTop
∀ (s : ℝ), Filter.Tendsto (fun x => Real.exp x / x ^ s) Filter.atTop Filter.atTop
The function exp(x) / x ^ s tends to +∞ at +∞, for any real number s.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- Filter.Tendstostatement · cited by 3,814
- Filter.atTopstatement and proof · cited by 2,405
- LT.lt.leproof · cited by 2,189
- le_reflproof · cited by 2,061
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- le_of_ltproof · cited by 1,175
- Real.expstatement and proof · cited by 871
- Real.exp_posproof · cited by 169
- Real.rpow_pos_of_posproof · cited by 155
- Filter.eventually_ge_atTopproof · cited by 111
Cited by1
Results whose statement or proof uses this declaration.
- tendsto_exp_mul_div_rpow_atTopproof · cited by 3