Theorems · Theorem · special functions
Real.tendsto_div_pow_mul_exp_add_atTop
∀ (b c : ℝ) (n : ℕ), 0 ≠ b → Filter.Tendsto (fun x => x ^ n / (b * Real.exp x + c)) Filter.atTop (nhds 0)
The function (x ^ n) / (b * exp x + c) tends to 0 at +∞, for any natural number
n and any real numbers b and c such that b is nonzero.
- Defined in
- Mathlib.Analysis.SpecialFunctions.Exp
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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
- mul_oneproof · cited by 3,885
- Filter.Tendstostatement and proof · cited by 3,814
- one_mulproof · cited by 2,841
- Filter.atTopstatement and proof · cited by 2,405
- neg_negproof · cited by 960
- one_ne_zeroproof · cited by 885
- Real.expstatement and proof · cited by 871
- neg_mulproof · cited by 654
- div_oneproof · cited by 629
Cited by3
Results whose statement or proof uses this declaration.
- tendsto_rpow_div_mul_addproof · cited by 2
- Real.tendsto_pow_log_div_mul_add_atTopproof · cited by 2
- Real.isLittleO_pow_exp_atTopproof · cited by 0