MATH 140 Lecture 5: Continuity and the I.V.T.
15 Sep 2015
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Math140 lecture 5 continuity and the intermediate value theorem. +n for all n, it is continuous at all x in its domain: a function f is continuous if it is continuous at every number in its domain, even if it is not defined at some numbers. Examples: ex 1: let f ( x)= x+2 x+1 , the function is defined and continuous at all x except for -1, ex 2: let g(x)= x . Is the function continuous at x = -3: the function is not continuous at x = -3 because the function is not defined at that number, ex 3: let h( x)= (x +2)(x +1) x +1. Is it continuous: cancel like terms: h( x)=x+2 , the function is a polynomial, therefore it is continuous. x= p. Is it continuous: the function is not continuous because, with these conditions, the function is discontinuous at every point x, ex 5: let p (x)={x ,x 2.
