MAT 21A Lecture 8: Math 21a Lecture 8 Continuous functions
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MAT 21A Full Course Notes
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Sum: f(x) + g(x) is continuous on (a, b). Product: f(x)g(x) is continuous on (a, b). Quotient: f(x)/g(x) is continuous on (a, b) provided g(x) 6= 0. Difference: f g is continuous on (a, b): continuous functions have the intermediate value property (ivp): suppose f is continuous on [a, b] and f(a) < < f(b). Then there exists such that a < < b with f( ) = . Useful for showing there exists a certain point satisfying an equation. e. g. root of an equation.