CALCULUS REVISION NOTES
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Limits describe the value a function approaches near an input.
Continuity at a requires lim(x->a) f(x) = f(a).
The derivative is the limit of [f(x+h)-f(x)]/h as h approaches zero.
Power rule: d(x^n)/dx = n*x^(n-1) where defined.
Product rule: (uv)' = u'v + uv'.
Chain rule: (f(g(x)))' = f'(g(x))*g'(x).
An indefinite integral describes a family of antiderivatives.
The fundamental theorem connects definite integration and derivatives.

Practice: differentiate x^3 + 2x; integrate 2x from 0 to 1.
Answers: 3x^2 + 2; 1.
Always check domain restrictions and the assumptions of each theorem.