1_5_infinite_limits_VA

1_5_infinite_limits_VA - 1.5 Infinite Limits and Vertical...

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Unformatted text preview: 1.5 Infinite Limits and Vertical Asymptotes p.88 # 1- 9, 13-27, 33-47, 59, 61 Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Title: Sep 177:45 PM (1 of 10) as x 1 from the right Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Title: Sep 177:38 PM (2 of 10) Find the vertical asymptotes. f(x): 2 VAs: x = 5 and x = 5 g(x): 1 VA: x = 5 for g(x), x = 5 is not VA, when substitute in numerator, get 0: 5 5 = 0 Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Title: Sep 177:47 PM (3 of 10) Since x = 1 results in denominator=0, and also numerator =0, x = 1 is NOT a VA. Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Title: Sep 192:45 PM (4 of 10) Continuity So, VA occurs where function is not continuous because the limits does not exist. Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Title: Sep 196:25 PM (5 of 10) For x = 2, numerator: x 1 0, so x = 2 is VA For x = 1, numerator: x 1 = 0, so x = 1 is NOT a VA (hole in graph) Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Title: Sep 196:30 PM (6 of 10) Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Title: Sep 196:37 PM (7 of 10) Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Title: Sep 196:42 PM (8 of 10) Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Title: Sep 196:46 PM (9 of 10) Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Title: Sep 196:50 PM (10 of 10) ...
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