Calculus
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38 minDerivatives · Implicit curves and related rates
Differentiate relationships without isolating y, find tangent slopes on curves, and connect changing geometric quantities.
40 minDerivatives · Composite functions and exponential bases
Work from the outside inward, differentiate nested functions, and derive the exponential rule for general positive bases.
39 minDerivatives · Products, quotients, tangent, and secant
Prove and apply the product and quotient rules, then derive the tangent and secant derivative formulas.
38 minDerivatives · Trigonometric and exponential functions
Derive the sine and cosine rules from limits, then prove the special derivative of ex and apply the new rules.
15 minDerivatives · Power, constant-multiple, and sum rules
Prove the power rule with the binomial theorem, then differentiate positive, negative, and fractional powers.
33 minDerivatives · Graphs, slopes, and corners
Turn tangent slopes into a derivative graph. Follow zeros, signs, and steepness, then check corners, endpoints, and vertical tangents.
41 minDerivatives · Tangent lines and rates
Build the derivative from secant-line limits, find tangent-line equations, and interpret instantaneous rates with their units.
29 minLimits · End behavior
Compare dominant powers, analyze exponential end behavior, and use a conjugate to evaluate a radical limit at infinity.
43 minLimits · Continuity and existence theorems
Trap an oscillating expression between simpler functions, test continuity at points and endpoints, and use IVT to prove that a zero exists.
36 minLimits · Trigonometry and piecewise functions
Use special trigonometric limits and identities, analyze one-sided limits, and choose a constant that makes a piecewise function continuous.
28 minLimits · Algebraic techniques
Use limit laws and direct substitution, then resolve indeterminate forms by factoring, rationalizing, and simplifying complex fractions.
32 minLimits · Tables and graphs
Compare one-sided limits, distinguish limits from function values, test continuity, and classify common discontinuities.
8 minApplications · Table estimates
Use secant slopes immediately before and after a target to estimate the tangent slope when no function formula is available.
35 minFoundations · Rates of change
Secant and tangent lines; rates and units; velocity versus speed; position functions; average velocity; and a first look at limits.
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