MATH 1ZB3 Lecture 6: 11.3 Integral Test and Sum Estimates
20 Feb 2019
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Es th honeheridncan4 sm chisonlyintega. tl m. t cnn. ie axiihiiiiit m. Is th isincreasingwith me e ii an e i fix d f if d bounded it ftix conte. 1 ie ancontr fz ancontr forlimitto n thestartingpoint don"t matte if5in an. In summary if use a bigger moearen integraltoforceconvergence oftheseries fly is positive contdecreasing an gnr. 1 shift egerieseneeeet tix function is stillpositive continuous decreasing. 3 4 5 t t b nd a du adu. Izzan 3 7 htt dx 2 let u x 11. O t"uidu an his e an his ifeng. gg hanitknugm diverges dicatethat1kseries which staff don"tmatter ifthis. D. mn also diverges r n noent because d fin is positive contdecreasing. In summary if use a smallerlesarea integral 6 force divergenceoftheseries if5in an then f tin dxd an dir. Hadpositive contdecay fix ztfx35v cont. fr 1135w dec lookat integral aslongascontinousstartpoint doesn"tmatter y. fitnxdx letn nx du dx. 2 an therefore j s3 e usingthepartumtoestimate fallen andusestheintegral tixdx to estimatethedifferencebetween.
