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Continuity Theorems

Continuity Theorems . If f and g are continuous at a and c is a constant, then the following are also continuous f + g f – g cf fg f/g if g≠0. Any polynomial is continuous everywhere: it is continuous from (-∞,∞)

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Continuity Theorems

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  1. Continuity Theorems

  2. If f and g are continuous at a and c is a constant, then the following are also continuous f + g f – g cf fg f/g if g≠0

  3. Any polynomial is continuous everywhere: it is continuous from (-∞,∞) Any rational function is continuous wherever it is defined; in other words it is continuous on its domain

  4. Example Where is the following continuous?

  5. The following functions are continuous everywhere on their domains Polynomials Rational functions Root functions Trig functions Inverse trig functions Exponential functions Logarithmic functions

  6. Example Where is the following continuous

  7. Theorem If f is continuous at b and then or

  8. Example: Find

  9. Theorem If f is continuous, then

  10. Theorem If g is continuous at a and f is continuous at g(a), then the composite function is continuous at a

  11. Example Where are the following continuous

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