References: Limits done carefully

Source material

Source curriculum (structural mirror, cited as further study):
This Clawdemy lesson bundles three consecutive 3Blue1Brown chapters into one,
because the three serve a single capability cluster (precise limits + handling
the forms where plug-in fails):
• 3Blue1Brown, Essence of Calculus, Chapter 8: "Limits and the definition of derivatives"
  https://www.3blue1brown.com/lessons/limits
• 3Blue1Brown, Essence of Calculus, Chapter 9: (ε, δ) "epsilon delta" definitions of limits
  https://www.3blue1brown.com/lessons/epsilon-delta
• 3Blue1Brown, Essence of Calculus, Chapter 10: "L'Hôpital's rule"
  https://www.3blue1brown.com/lessons/l-hopitals-rule
  Creator: Grant Sanderson
  Series index: https://www.3blue1brown.com/?topic=calculus
  License: copyright Grant Sanderson; videos published on his site and YouTube
Clawdemy's lessons are original prose that follows the pedagogical arc of this
series. We do not reproduce or transcribe the videos; we cite them as the
recommended companion. All rights to the original videos remain with the creator.

Watch this next

Limits and the definition of derivatives (3Blue1Brown) by Grant Sanderson. The first of the three chapters this lesson bundles. It connects the limit directly back to the derivative definition, showing the 0/0 form the rate ratio produces.
(ε, δ) definitions of limits. The precise definition, where the “for any precision, a window exists” idea is made visual.
L’Hôpital’s rule. The practical tool for 0/0 and ∞/∞, with the leading-behavior intuition for why it works.

Going deeper

Essence of Calculus (full series) by 3Blue1Brown. The series this track follows. The previous Clawdemy lesson covered implicit differentiation; the next chapter (Integration and the fundamental theorem of calculus) turns from rates to accumulation.
Khan Academy: Calculus for a slower, exercise-driven treatment of limits, the epsilon-delta definition, and L’Hôpital’s rule, with practice problems and immediate feedback.

Adjacent topics

Where this sits in the track and the wider curriculum.

The derivative as a rate (earlier lesson). That lesson defined the derivative as lim (h->0) (f(x+h)-f(x))/h, a 0/0 limit handled by simplifying before taking the limit. This lesson is the foundation underneath it: what “approaches” means, and how to compute the limits that resist a plug-in.
Taylor series (final lesson). L’Hôpital works by keeping each function’s first-order behavior near a point (f(a) + f'(a)(x-a)). Taylor series extends that to a full polynomial built from all the derivatives, so L’Hôpital is the one-term preview of the capstone.
Convergence and approximation theory (across the AI tracks). The guarantees that gradient descent converges and that neural networks can approximate arbitrary functions are limit-based statements; the “forceable arbitrarily close” intuition here is the same one those proofs rely on.