CalcRef · 14 guides
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A plain-English guide to limits in calculus: what "approaching a value" really means, why 0/0 is not the end of the story, and how one-sided limits and infinity fit in.
7 min read
Read guideA narrative cheat-guide to the derivative rules: power, constant, sum, product, quotient, and chain rules, explained in learning order with when-to-use guidance.
8 min read
Read guideA decision guide for integration: when to use u-substitution, integration by parts, trig substitution, or partial fractions, with the tell-tale signs for each method.
8 min read
Read guideThe recurring errors that lose points in calculus: dropping the chain rule, sign slips in the quotient rule, 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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