Theorems · Theorem · real analysis

deriv.lhopital_zero_nhdsLT

∀ {a : ℝ} {l : Filter ℝ} {f g : ℝ → ℝ},
  (∀ᶠ (x : ℝ) in nhdsWithin a (Set.Iio a), DifferentiableAt ℝ f x) →
    (∀ᶠ (x : ℝ) in nhdsWithin a (Set.Iio a), deriv g x ≠ 0) →
      Filter.Tendsto f (nhdsWithin a (Set.Iio a)) (nhds 0) →
        Filter.Tendsto g (nhdsWithin a (Set.Iio a)) (nhds 0) →
          Filter.Tendsto (fun x => deriv f x / deriv g x) (nhdsWithin a (Set.Iio a)) l →
            Filter.Tendsto (fun x => f x / g x) (nhdsWithin a (Set.Iio a)) l

L'Hôpital's rule for approaching a real from the left, deriv version

Defined in

Mathlib.Analysis.Calculus.LHopital

Cited by

0 results in Mathlib

Foundations

Depth 194 from the axioms · uses propext, Classical.choice, Quot.sound