1-4 Continuity and One Sided Limits Notes

Testeachequationatthexvalueintherestrictions

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Unformatted text preview: non­removable. Breaks, that aren't holes or vertical asymptotes, in a graph usually occur in piecewise functions at the x­values where the function changes equations. Test each equation at the x­value in the restrictions. Asymptotes and trig functions tangent and secant parent graph's asymptotes: , ..... , , ..... cosecant and cotangent parent graph's asymptotes: . . . , , . . . 3 1­4 Continuity and One Sided Limits Notes 2012 Discontinuities: hole 1) removable ex asymptote break 2) nonremovable ex 4 1­4 Continuity and One Sided Limits Notes 2012 Ex 1: Discuss the continuity of each function: a) b) c) y=sinx 5 1­4 Continuity and One Sided Limits Notes 2012 One­sided Limits lim f(x) = L ⇒ approaching from the right + x c lim f(x) = L ⇒ approaching from the left ­ x c ***useful with functions with restricted domain*** Ex 2 : a) b) not appropriate to talk about the limit from the left. 6 1­4 Continuity and One Sided Limits Notes 2012 Ex 3 : Greatest Integer Function greatest integer that is less than or equal to the value given 7 1­4 Continuity and One Sided Limits Notes 2012 Existence of a Limit : Let f be a function and let c and L be real numbers. The limit of f(x) as x approaches c is L if and only i...
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This note was uploaded on 05/01/2013 for the course MATH Calculus H taught by Professor Pearson during the Fall '12 term at Wwindsor Plainsboro South.

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