Theorems · Theorem · special functions
Real.tendsto_exp_div_pow_atTop
∀ (n : ℕ), Filter.Tendsto (fun x => Real.exp x / x ^ n) Filter.atTop Filter.atTop
The function exp(x)/x^n tends to +∞ at +∞, for any natural number n
- Defined in
- Mathlib.Analysis.SpecialFunctions.Exp
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites41
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
- mul_oneproof · cited by 3,885
- Filter.Tendstostatement · cited by 3,814
- Nat.cast_oneproof · cited by 2,501
- Filter.atTopstatement · cited by 2,405
- LT.lt.leproof · cited by 2,189
- add_commproof · cited by 1,535
- Set.Ioiproof · cited by 1,463
- LT.lt.ne'proof · cited by 1,417
- le_of_ltproof · cited by 1,175
- Real.expstatement and proof · cited by 871
- LE.le.trans_ltproof · cited by 795
Cited by3
Results whose statement or proof uses this declaration.
- Real.tendsto_pow_mul_exp_neg_atTop_nhds_zeroproof · cited by 1
- Real.tendsto_mul_exp_add_div_pow_atTopproof · cited by 1
- tendsto_exp_div_rpow_atTopproof · cited by 1