Calculus, worked out

The Rate Machine′

Calculus is the math of change. Find a limit (and see what to do when plugging in gives 0/0), differentiate with the power, product, quotient and chain rules, find tangent lines, maxima and minima, antiderivatives and areas, and rates of change — one rule per line, with the reason for every step.

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The work

Say it out loud

    Everything is worked out exactly: fractions stay fractions, and √, π, e and ln stay as they are. Graphing a function first? See the graph paper. Powers and roots: the power tower.