Section_1.4_Day_1_Notes

Section_1.4_Day_1_Notes - 8/26/201 1 Calculus AP—AB...

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Unformatted text preview: 8/26/201 1 Calculus AP—AB August 26, 2011 Section 1.4 ' Limits approach from both sides!’ If the two sides doh’t. match, the limit does not exist, unless. you only want to, or are able to approach from one side ‘. __ ~ 4 F 4' Objective: Evaluate one—sided limits a- Begin by ignoring the left and right hand limit when you plug in,_ but sometimes it matters: Square roots Absolute value Piecewise functions Greatest integer functions 8/26/2011 Does the function exist left of 1? Does the limit exist at 1? lim |x—1i+2= 7, :H iim lx—1i+2: ’Z/ \¥I 11:31l |x—ii+2: 1/ w/0 3'41?" N“?"*“ I?” ‘3 PEQQE ufiSfl “muffin xr' *1 X7. "m ... [M xLI_“»‘ y-xpi 4Xh1){1 )Lél [3M —)LJ‘3 :21 8/26/2011 Does the requested limit exist? Greatest integer function llxllr the greatest integer less than or equal to x Think “left of” each integer on a numberline 8/26/2011 Does the limit exist at 2? At 1? Definition of Continuity Continuity at a point: A function f is continuous at x : c, if 3 conditions are met. 1 .f(c) exists 2. lim f(x) exists x—ar i 3. 1imf(x) = f(c) % 63/269011 ...
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Section_1.4_Day_1_Notes - 8/26/201 1 Calculus AP—AB...

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