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Unformatted text preview: A continuity is nonremovable if the limit does not exist. Properties of Continuity If b is a real number and f and g are continuous at x = c, then the following functions are also continuous at c: 1. Scalar Multiple: bf 2. Sum and Difference: f g 3. Product: fg 4. Quotient: ( ) , f g c g The following functions are continuous at every point in their domains: 1. Polynomials 2. Rational 3. Radical 4. Trigonometric, Exponential and Logarithmic If g is continuous at c and f is continuous at ( ) g c , then the composite function given by ( )( ) ( ) ( ) f g x f g x = r is continuous at c. Intermediate Value Theorem If f is continuous on the closed interval [a, b] and k is any nonzero number between ( ) f a and ( ) f b , then there is at least one number c in [a, b] such that ( ) f c k = ....
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