# CalculusKitzo (calculus.kitzo.work)

> CalculusKitzo is a free, independent, interactive calculus tutoring website. It covers the classic single-variable calculus syllabus across 32 crawlable sections (chapters plus appendices), with 256 auto-marked exercises. Every lesson is server-rendered; every chapter also has a plain-Markdown mirror for retrieval and citation.

## Key facts
- Website: https://calculus.kitzo.work/
- Language: English
- Price: free; no account required to read or practice (email + 6-digit code sign-in only syncs progress)
- Audience: high-school (AP Calculus AB/BC, A-level, IB) and first-year university students, self-learners in STEM
- Stack: server-rendered HTML + Cloudflare Workers + D1 (100% Cloudflare, no third-party APIs)
- Content: original lessons, worked examples, hints and exercises; not copied from any textbook

## Canonical pages
- Home: https://calculus.kitzo.work/
- Extended AI briefing: https://calculus.kitzo.work/llms-full.txt
- XML sitemap: https://calculus.kitzo.work/sitemap.xml
- Disclaimer, citation & sources: https://calculus.kitzo.work/disclaimer

## Chapter index (HTML + Markdown)
- [Chapter 1: Functions, Graphs and Lines](https://calculus.kitzo.work/chapter/functions) · [Markdown](https://calculus.kitzo.work/chapter/functions.md) — The vocabulary of calculus: what a function is, how to read graphs, domain and range, inverses, composition, odd/even symmetry, linear functions and the menagerie of standard graphs.
- [Chapter 2: Review of Trigonometry](https://calculus.kitzo.work/chapter/trigonometry) · [Markdown](https://calculus.kitzo.work/chapter/trigonometry.md) — Radians and the unit circle, ASTC signs, trig beyond [0, 2π), graphs of the six trig functions, special-angle values, the identities that power calculus, and simple trig equations.
- [Chapter 3: Introduction to Limits](https://calculus.kitzo.work/chapter/limits-intro) · [Markdown](https://calculus.kitzo.work/chapter/limits-intro.md) — What a limit really is, one-sided limits, the ways limits fail to exist, limits at ±∞, vertical and horizontal asymptotes done correctly, and the Sandwich Principle with sin x / x near 0.
- [Chapter 4: Solving Limit Problems Involving Polynomials](https://calculus.kitzo.work/chapter/limits-polynomials) · [Markdown](https://calculus.kitzo.work/chapter/limits-polynomials.md) — The workhorse toolkit for hands-on limit problems: factor and cancel at finite points, the conjugate trick for square roots, divide by the highest power at infinity, degree comparison, and absolute-value and one-sided infinite limits.
- [Chapter 5: Continuity and Differentiability](https://calculus.kitzo.work/chapter/continuity) · [Markdown](https://calculus.kitzo.work/chapter/continuity.md) — From continuity at a point and on intervals, through IVT and the Extreme Value Theorem, to velocity vs speed, tangent lines, the derivative as a limit of the difference quotient, the second derivative, and when derivatives fail to exist.
- [Chapter 6: How to Solve Differentiation Problems](https://calculus.kitzo.work/chapter/differentiation) · [Markdown](https://calculus.kitzo.work/chapter/differentiation.md) — Every differentiation rule you will ever use flows from a single limit. Learn the definition, then the shortcuts it powers — from product and quotient rules to tangent lines, velocity and curve-sketching.
- [Chapter 7: Trig Limits and Derivatives](https://calculus.kitzo.work/chapter/trig-derivatives) · [Markdown](https://calculus.kitzo.work/chapter/trig-derivatives.md) — One geometric limit — sin θ over θ — powers every trig derivative in the syllabus, from sin x to sin(x²) to the acceleration a = −ω²x of anything oscillating.
- [Chapter 8: Implicit Differentiation and Related Rates](https://calculus.kitzo.work/chapter/implicit-differentiation) · [Markdown](https://calculus.kitzo.work/chapter/implicit-differentiation.md) — Not every curve lets you solve for y. Implicit differentiation unlocks circles, trig curves and more — and the same move, differentiated with respect to time, powers every related-rates problem.
- [Chapter 9: Exponentials and Logarithms](https://calculus.kitzo.work/chapter/exponentials-logs) · [Markdown](https://calculus.kitzo.work/chapter/exponentials-logs.md) — From compound interest to radioactive decay, everything that grows or dies exponentially is governed by one constant: e. Meet e, its mirror image ln x, their derivatives, and the models they drive.
- [Chapter 10: Inverse Functions and Inverse Trig Functions](https://calculus.kitzo.work/chapter/inverse-functions) · [Markdown](https://calculus.kitzo.work/chapter/inverse-functions.md) — When is a function invertible, and how fast does its inverse grow? The answer to both questions lives in the derivative — no inverting required.
- [Chapter 11: The Derivative and Graphs](https://calculus.kitzo.work/chapter/derivative-graphs) · [Markdown](https://calculus.kitzo.work/chapter/derivative-graphs.md) — Turn derivatives into a full profile of a function: locate global and local extrema, prove Rolle's and the Mean Value Theorem, and read concavity straight off the second derivative.
- [Chapter 12: Sketching Graphs](https://calculus.kitzo.work/chapter/sketching-graphs) · [Markdown](https://calculus.kitzo.work/chapter/sketching-graphs.md) — Learn the sign-table craft: read increasing/decreasing from f′ and concavity from f″, then assemble any function into a reliable sketch using the Big Method.
- [Chapter 13: Optimization and Linearization](https://calculus.kitzo.work/chapter/optimization) · [Markdown](https://calculus.kitzo.work/chapter/optimization.md) — A complete method for constrained best-and-worst problems, from fencing a garden to cone-in-sphere puzzles — plus linearization, differentials, error bounds, and Newton's method.
- [Chapter 14: L'Hôpital's Rule and Overview of Limits](https://calculus.kitzo.work/chapter/lhopital) · [Markdown](https://calculus.kitzo.work/chapter/lhopital.md) — Master the indeterminate forms 0/0 and ∞/∞, convert ∞−∞, 0·∞ and exponential forms with algebra and logarithms, and see the whole limit toolkit in one map.
- [Chapter 15: Introduction to Integration](https://calculus.kitzo.work/chapter/integration-intro) · [Markdown](https://calculus.kitzo.work/chapter/integration-intro.md) — Sigma notation, telescoping sums, displacement versus distance, signed area, and the leap from rectangular approximation to the definite integral.
- [Chapter 16: Definite Integrals](https://calculus.kitzo.work/chapter/definite-integrals) · [Markdown](https://calculus.kitzo.work/chapter/definite-integrals.md) — Area as a limit: the definition of ∫ₐᵇ f(x)dx via Riemann sums, careful properties and sign conventions, true areas with absolute values, area between curves, upper and lower estimates, and the average value theorem.
- [Chapter 17: The Fundamental Theorems of Calculus](https://calculus.kitzo.work/chapter/ftc) · [Markdown](https://calculus.kitzo.work/chapter/ftc.md) — The bridge between differentiation and integration: accumulation functions F(x) = ∫ₐˣ f(t)dt, the First FTC (F′ = f), antiderivatives, the Second FTC (top minus bottom), the four classic F′ variations, and unsigned area via splitting at zeros.
- [Chapter 18: Integration Techniques, Part One](https://calculus.kitzo.work/chapter/integration-1) · [Markdown](https://calculus.kitzo.work/chapter/integration-1.md) — The workhorses of integration: u-substitution (indefinite and with changed limits), the inside-function rule, integration by parts with LIATE, and partial fractions — distinct, repeated and irreducible-quadratic factors — capped by one big worked example.
- [Chapter 19: Integration Techniques, Part Two](https://calculus.kitzo.work/chapter/integration-2) · [Markdown](https://calculus.kitzo.work/chapter/integration-2.md) — When substitution and parts run out of road: trig identities (sin²x, cos²x), parity rules for powers of sin/cos/tan/sec, the three trig substitutions for square roots (sine, tangent, secant), and completing the square — with a summary table.
- [Chapter 20: Improper Integrals: Basic Concepts](https://calculus.kitzo.work/chapter/improper-integrals-concepts) · [Markdown](https://calculus.kitzo.work/chapter/improper-integrals-concepts.md) — When the interval is infinite or the integrand blows up, do we still get a finite answer? This chapter answers it: convergence versus divergence, and the four tests that decide.
- [Chapter 21: Improper Integrals: How to Solve Problems](https://calculus.kitzo.work/chapter/improper-integrals-solving) · [Markdown](https://calculus.kitzo.work/chapter/improper-integrals-solving.md) — A field guide to improper integrals: split at every blow-up, compare against p-integrals, and read off convergence — without ever finishing the integral.
- [Chapter 22: Sequences and Series: Basic Concepts](https://calculus.kitzo.work/chapter/sequences-series) · [Markdown](https://calculus.kitzo.work/chapter/sequences-series.md) — From convergent sequences to geometric growth: what convergence means, the tests series obey, and why the improper-integral playbook transfers wholesale.
- [Chapter 23: How to Solve Series Problems](https://calculus.kitzo.work/chapter/series-solving) · [Markdown](https://calculus.kitzo.work/chapter/series-solving.md) — A mechanical toolkit: nth-term first, then geometric, ratio, root, comparison and integral tests — plus a flowchart for any series you meet.
- [Chapter 24: Taylor Polynomials, Taylor Series, and Power Series](https://calculus.kitzo.work/chapter/taylor-series) · [Markdown](https://calculus.kitzo.work/chapter/taylor-series.md) — Build any smooth function from polynomials: Taylors at a point, Maclaurin series, power series — and when they do (and don’t) equal the function.
- [Chapter 25: How to Solve Estimation Problems](https://calculus.kitzo.work/chapter/taylor-estimation) · [Markdown](https://calculus.kitzo.work/chapter/taylor-estimation.md) — When is your approximation actually accurate? Remainder bounds, alternating-series estimates, and five fully-worked estimation problems.
- [Chapter 26: Taylor and Power Series: How to Solve Problems](https://calculus.kitzo.work/chapter/power-series) · [Markdown](https://calculus.kitzo.work/chapter/power-series.md) — Radius and intervals of convergence, and how to bend known series — by substituting, differentiating, integrating and combining — into derivatives, integrals and limits that l'Hôpital cannot touch.
- [Chapter 27: Parametric Equations and Polar Coordinates](https://calculus.kitzo.work/chapter/parametric-polar) · [Markdown](https://calculus.kitzo.work/chapter/parametric-polar.md) — Curves driven by a parameter or an angle: parametric derivatives, speed, the polar toolkit — conversions, cardioids, limaçons, roses — polar tangents, and area via A = ½∫r² dθ.
- [Chapter 28: Complex Numbers](https://calculus.kitzo.work/chapter/complex-numbers) · [Markdown](https://calculus.kitzo.work/chapter/complex-numbers.md) — From i to Euler's formula: arithmetic, conjugates and moduli, the complex plane, De Moivre powers, all n roots of zⁿ = w, logarithms of complex numbers — and why e^(iπ) + 1 = 0 is the jewel of the subject.
- [Chapter 29: Volumes, Arc Lengths, and Surface Areas](https://calculus.kitzo.work/chapter/applications-integrals) · [Markdown](https://calculus.kitzo.work/chapter/applications-integrals.md) — Discs, washers, shells and cross-sections for volumes of revolution, plus arc length and surface area — the full toolkit for turning flat regions into exact 3D measurements.
- [Chapter 30: Differential Equations](https://calculus.kitzo.work/chapter/differential-equations) · [Markdown](https://calculus.kitzo.work/chapter/differential-equations.md) — Equations with derivatives: separable, linear (integrating factors), constant-coefficient second order — plus the modeling loop.
- [Chapter A: Appendix A: Limits and Proofs (ε–δ)](https://calculus.kitzo.work/chapter/epsilon-delta) · [Markdown](https://calculus.kitzo.work/chapter/epsilon-delta.md) — The formal definition of a limit — the ε–δ game — and how it proves the limit laws you have been using all along.
- [Chapter B: Appendix B: Estimating Integrals](https://calculus.kitzo.work/chapter/appendix-b) · [Markdown](https://calculus.kitzo.work/chapter/appendix-b.md) — When the antiderivative is impossible or painful: strips, the trapezoidal rule, Simpson’s rule — and honest error bounds.

## Citation & reuse policy
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