Theorems · Theorem · real analysis

HasDerivAt.lhopital_zero_atTop_on_Ioi

∀ {a : ℝ} {l : Filter ℝ} {f f' g g' : ℝ → ℝ},
  (∀ x ∈ Set.Ioi a, HasDerivAt f (f' x) x) →
    (∀ x ∈ Set.Ioi a, HasDerivAt g (g' x) x) →
      (∀ x ∈ Set.Ioi a, g' x ≠ 0) →
        Filter.Tendsto f Filter.atTop (nhds 0) →
          Filter.Tendsto g Filter.atTop (nhds 0) →
            Filter.Tendsto (fun x => f' x / g' x) Filter.atTop l → Filter.Tendsto (fun x => f x / g x) Filter.atTop l

Defined in

Mathlib.Analysis.Calculus.LHopital

Cited by

3 results in Mathlib

Foundations

Depth 188 from the axioms · uses propext, Classical.choice, Quot.sound