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# lecture8 - Lecture 8 1 Lecture 8 Sec 2.5 One-Sided Limits...

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Lecture 8 1 Lecture 8: Sec. 2.5 One-Sided Limits, Unbounded Functions and Continuity ex. f ( x ) = braceleftbigg x 2 + 1 if x< 0 x 1 if x 0 How do we find lim x 0 f ( x )?

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Lecture 8 2 Def. One - Sided Limits 1) lim x a f ( x ) 2) lim x a + f ( x ) For our example, lim x 0 + f ( x ) = and lim x 0 f ( x ) = Theorem : lim x a f ( x ) = L if and only if
Lecture 8 3 ex. f ( x ) = braceleftbigg x 2 + 1 if x< 0 x + 1 if x> 0 Evaluate lim x 0 f ( x ).

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Lecture 8 4 Continuity Consider the function y = f ( x ) graphed below:
Lecture 8 5 Evaluate the following: 1) f ( 2) = lim x →− 2 f ( x ) = 2) f ( 1) = lim x →− 1 f ( x ) = 3 f (4) = lim x 4 f ( x ) = 4) f (6) = lim x 6 f ( x ) = For which x -values is f ( x ) not continuous ?

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Lecture 8 6 Def. A function f is continuous at the point x = a if: 1) 2) 3) A function is continuous on the open interval ( a,b ) if
Lecture 8 7 Properties of Continuous Functions (p. 123) If functions f and g are continuous at x = a , then each of the following are also continuous at x = a : 1) f ± g 2) kf , where k is any nonzero real number 3) fg 4) f g , where g ( a ) negationslash = 0

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lecture8 - Lecture 8 1 Lecture 8 Sec 2.5 One-Sided Limits...

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