CalcRef · 14 guides
CalcRef guides are in-depth calculus explainers for students, written around the same formula database you can browse and drill in CalcRef. Each one covers a single topic, such as limits, the derivative rules or choosing an integration technique, with the key formulas and a short FAQ. Every guide is free, no account required.
A plain-English guide to limits: what "approaching a value" really means, why 0/0 is not the end of the story, and where one-sided limits and infinity fit.
7 min read
Read guideThe derivative rules in the order you learn them: power, constant, sum, product, quotient and chain rules, each with when-to-use guidance.
8 min read
Read guideWhen to use u-substitution, integration by parts, trig substitution or partial fractions, with the tell-tale signs that point to each method.
8 min read
Read guideThe recurring calculus errors that lose points: dropping the chain rule, quotient rule sign slips, forgetting +C, and confusing a function with its limit.
7 min read
Read guideA week-by-week plan for passing Calculus 1: what to master in each unit, how to practice efficiently, and where students most often fall behind.
8 min read
Read guideA decision guide to the convergence tests: divergence, geometric, p-series, ratio, root, comparison, integral, and alternating, with the tell for each.
8 min read
Read guideA clear method for related rates problems: how to connect changing quantities, differentiate with respect to time, and avoid the classic setup mistakes.
7 min read
Read guideA complete guide to u-substitution: how it reverses the chain rule, how to choose u, and how to handle definite integrals and the limits of integration.
7 min read
Read guideHow to find dy/dx when y isn't solved for explicitly: the chain-rule trick, a step-by-step method, worked examples, and implicit second derivatives.
7 min read
Read guideA step-by-step method for calculus optimization problems: build the objective function, apply the constraint, and confirm the extremum.
7 min read
Read guideWhat both parts of the Fundamental Theorem of Calculus say, why derivatives and integrals are inverses, and how to differentiate a variable-limit integral.
8 min read
Read guideHow to set up area-between-curves integrals, when to integrate in y, and how to choose between disks, washers, and cylindrical shells for volumes.
8 min read
Read guideWhy Taylor series work, where the factorials come from, the standard Maclaurin series to memorize, and how to bound the error with the Lagrange remainder.
8 min read
Read guideHow to find the radius of convergence with the ratio test, why both endpoints need separate checks, and what term-by-term calculus does to the interval.
8 min read
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