Theorems · Theorem · real analysis
tendsto_exp_mul_div_rpow_atTop
∀ (s b : ℝ), 0 < b → Filter.Tendsto (fun x => Real.exp (b * x) / x ^ s) Filter.atTop Filter.atTop
The function exp (b * x) / x ^ s tends to +∞ at +∞, for any real s and b > 0.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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 · cited by 2,405
- mul_commproof · cited by 2,262
- LT.lt.leproof · cited by 2,189
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- LT.lt.ne'proof · cited by 1,417
- Real.expstatement and proof · cited by 871
- Filter.Tendsto.compproof · cited by 560
- Real.exp_posproof · cited by 169
- Filter.Tendsto.congr'proof · cited by 154
Cited by3
Results whose statement or proof uses this declaration.
- isLittleO_exp_neg_mul_rpow_atTopproof · cited by 4
- tendsto_rpow_mul_exp_neg_mul_atTop_nhds_zeroproof · cited by 4
- Real.Gamma_integrand_isLittleOproof · cited by 2