Formula reference
A compact index of high-use formulas with hypotheses and interpretation prompts.
A formula is useful only with its hypotheses. Use this page for retrieval after you can derive or explain the result in its course.
| Idea | Statement | Conditions to check |
|---|---|---|
| Quadratic roots | \(x=(-b\pm\sqrt{b^2-4ac})/(2a)\) | \(a\ne0\); real versus complex domain |
| Derivative definition | \(f'(a)=\lim_{h\to0}[f(a+h)-f(a)]/h\) | The limit exists and is finite |
| Fundamental Theorem | \(\int_a^b f(x)\,dx=F(b)-F(a)\) | \(f\) continuous; \(F'=f\) on the interval |
| Bayes’ rule | \(P(A\mid B)=P(B\mid A)P(A)/P(B)\) | \(P(B)>0\) |
| Standardization | \(z=(x-\mu)/\sigma\) | \(\sigma>0\); interpretation depends on model |
Add formulas to your own reference with a derivation, units, failure cases, and one example. A bare formula list encourages unsafe pattern matching.
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