Theorems · Theorem · sequences and series
tendsto_mul_add_inv_atTop_nhds_zero
∀ (a c : ℝ), a ≠ 0 → Filter.Tendsto (fun x => (a * x + c)⁻¹) Filter.atTop (nhds 0)
If a ≠ 0, (a * x + c)⁻¹ tends to 0 as x tends to ∞.
- Defined in
- Mathlib.Analysis.SpecificLimits.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- nhdsstatement · cited by 5,554
- Filter.Tendstostatement · cited by 3,814
- Filter.atTopstatement and proof · cited by 2,405
- Filter.Tendsto.compproof · cited by 560
- Filter.tendsto_idproof · cited by 180
- lt_or_gt_of_neproof · cited by 41
- Filter.Tendsto.const_mul_atTopproof · cited by 30
- Filter.tendsto_atTop_add_const_rightproof · cited by 20
- tendsto_inv_atTop_zeroproof · cited by 19
- Filter.Tendsto.const_mul_atTop_of_negproof · cited by 9
- Filter.tendsto_atBot_add_const_rightproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Real.tendsto_pow_logb_div_mul_add_atTopproof · cited by 1