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Unformatted text preview: Lecture 7 Evaluating Limits Recall that if a function f is continuous at a , then lim x a f ( x ) = f ( a ) . Thus, it is easy to evaluate limits for continuous functions. What types of functions are continuous? Theorem: The following functions are continuous on every interval in their domains: Absolute Value Function, Root Functions, Polynomials, Rational Functions, Exponential Functions, Trigonometric Functions, Logarithmic Functions, and the Inverse Trigonometric Functions. We can now combine these to produce even more continuous functions using the following theorems for the algebra of functions: Theorem: If functions f and g are continuous at a and if c and d are any constants, then the functions cf + dg and fg are continuous at a . The function f g is continuous at a provided that g ( a ) 6 = 0 . Theorem: If g is continuous at a and f is continuous at g ( a ) , then f g is continuous at a . Identify the interval(s) on which each function is continuous: G ( x ) = e x ln( x ) H ( t ) = 1- t 2 t Evaluate:...
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