1_4continuity - 1_4_continuity_web2009.notebook Homework...

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Unformatted text preview: 1_4_continuity_web2009.notebook September 21, 2009 Homework for Section 1.4, Continuity and Onesided Limits Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework on the Web Part 1 Part 2 INTRO, homework How would you describe the graph of a curve that is continuous on an interval? Your thoughts: Students in class: Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework on the Web Part 1 Part 2 Sep 104:48 PM 1 1_4_continuity_web2009.notebook September 21, 2009 Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework on the Web Part 1 Part 2 Sep 104:50 PM Not defined at x = 3, so there is an opening in the graph at (3,6) Therefore, NO, NOT CONTINUOUS for all x but YES, CONTINUOUS on ( , 3) U (3, ) Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework on the Web Part 1 Part 2 Sep 104:50 PM 2 1_4_continuity_web2009.notebook September 21, 2009 Therefore, NO, NOT CONTINUOUS for all x but YES, CONTINUOUS on ( , 3) U (3, ) Not defined at x = 3, so there is an opening in the graph at (3,6) What happens to y as x > 3 from either side? Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework on the Web Part 1 Part 2 Sep 104:50 PM What is needed for continuity at a point? Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework on the Web Part 1 Part 2 Sep 104:52 PM 3 1_4_continuity_web2009.notebook September 21, 2009 Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework on the Web Part 1 Part 2 Sep 167:36 PM s Required to show continuity. Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework on the Web Part 1 Part 2 Sep 104:52 PM 4 1_4_continuity_web2009.notebook September 21, 2009 What about continuity on an interval? Consider f(x) = (9x2) g(x) = 1 (9x2) Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework on the Web Part 1 Part 2 Sep 104:53 PM What about continuity on an interval? Consider f(x) = (9x2) g(x) = 1 (9x2) I. A function is continuous on an open interval (a,b) if it is continuous at each point in (a,b). II. A function is continuous on an closed interval [a,b] if it is continuous at each point in (a,b), and lim f(x) = f(a) and lim f(x) = f(b) x>a+ x>b III. Functions continuous on entire real number line is everywhere continuous. Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework on the Web Part 1 Part 2 Sep 104:53 PM 5 1_4_continuity_web2009.notebook #39 September 21, 2009 Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework on the Web Part 1 Part 2 Sep 105:04 PM Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework on the Web Part 1 Part 2 Sep 177:04 PM 6 1_4_continuity_web2009.notebook September 21, 2009 Sep 177:04 PM Sep 1612:13 PM 7 ...
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