Theorems · Theorem · real analysis
tendsto_rpow_div_mul_add
∀ (a b c : ℝ), 0 ≠ b → Filter.Tendsto (fun x => x ^ (a / (b * x + c))) Filter.atTop (nhds 1)
The function x ^ (a / (b * x + c)) tends to 1 at +∞, for any real numbers a, b, and
c such that b is nonzero.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
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 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
- MulZeroClass.mul_zeroproof · cited by 2,091
- Set.Ioiproof · cited by 1,463
- Real.logproof · cited by 939
- pow_oneproof · cited by 894
- one_ne_zeroproof · cited by 885
- Real.expproof · cited by 871
Cited by2
Results whose statement or proof uses this declaration.
- tendsto_rpow_divproof · cited by 0
- tendsto_rpow_neg_divproof · cited by 0