Calculus Theorems on Continuity

This video introduces some of the important continuity theorems used in calculus. We begin by talking about the algebra of continuous functions and then use the fact that x is continuous to build up that polynomials and rational functions are continuous. We then introduce a list of functions continuous on their domains:
• Polynomials
• Rational Functions
• Trigonometric Functions
• Inverse Trigonometric Functions
• Exponential Functions
• Logarithmic Functions
• Radicals
• Absolute value

We then move on to a theorem stating that the composition of continuous functions is continuous before moving on to three examples including a rational function, a half circle, and a composite function – we find the domains on which they are continuous.

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