Theorems · Theorem · real analysis

HasDerivAt.lhopital_zero_right_on_Ioo

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

Defined in

Mathlib.Analysis.Calculus.LHopital

Cited by

5 results in Mathlib

Foundations

Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound