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Mathematics

The Implicit Function Theorem and Its Applications in Calculus

Quick fact

The implicit function theorem guarantees that even when you cannot solve an equation like x^2 + y^2 = 1 for y as a single formula, there exists a local function y = f(x) near almost every point on the curve.

Why this is interesting

Have you ever wondered how we can describe a curve like a circle as a function, even though it's not a function of x? The implicit function theorem holds the answer.