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.

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Presentation transcript:

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 (-∞,∞) Any rational function is continuous wherever it is defined; in other words it is continuous on its domain

Example Where is the following continuous?

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

Example Where is the following continuous

Theorem If f is continuous at b and then or

Example: Find

Theorem If f is continuous, then

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

Example Where are the following continuous