Taylor and Maclaurin Series
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1 Taylor ad Maclauri Sris Taylor ad Maclauri Sris Thory sctio which dals with th followig topics: - Th Sigma otatio for summatio. - Dfiitio of Taylor sris. - Commo Maclauri sris. - Taylor sris ad Itrval of covrgc. Basic Erciss with Maclauri Sris Qustios: ) Fid th Taylor sris of f si aroud. (Us th tabl of Maclauri pasios i th Appdi) 4 ) Fid th Taylor sris of f aroud. (Us th tabl of Maclauri pasios i th Appdi) ) Fid th Taylor sris of f sih aroud. (Us th tabl of Maclauri pasios i th Appdi) 4) Fid th Taylor sris of f si aroud. (Us th tabl of Maclauri pasios i th Appdi) 5) Fid th Taylor sris of f cos aroud. (Us th tabl of Maclauri pasios i th Appdi) 6) Fid th Taylor sris of f aroud. (Us th tabl of Maclauri pasios i th Appdi) Th bst way to gt a A Gt vido solutios for this workbook at
2 7) Fid th Taylor sris of f cos 4 aroud. (Us th tabl of Maclauri pasios i th Appdi) 8) Fid th Taylor sris of f l aroud. (Us th tabl of Maclauri pasios i th Appdi) 9) Fid th Taylor sris of f arcsi aroud. (Us th tabl of Maclauri pasios i th Appdi). Epasios about Gral Poit Qustios: ) Fid th Taylor sris of f l pdd aroud. ) Fid th Taylor sris of f pdd aroud. ) Fid th Taylor sris of si f pdd aroud. Fidig Nozro Trms i Epasios Qustios: ) Fid th first four ozro trms of th Maclauri sris of f cos. 4) Fid th first four ozro trms of th Maclauri sris of f ta. 5) Fid th first four ozro trms of th Maclauri sris of f si. Th bst way to gt a A Gt vido solutios for this workbook at
3 Sum of Sris Usig Taylor ad Maclauri Epasios Qustios: 6) Comput th sum of th followig sris:..!.!! 7) Comput th sum of th followig sris: 8) Comput th sum of th followig sris: 9) Comput th sum of th followig sris: ) Comput th sum of th followig sris: ) Comput th sum of th followig sris: ) Comput th sum of th followig sris:.!..!.!.. Fidig Limits Usig Epasios Qustios: ) Comput th valu of th followig limit: arcta a. lim si b. lim 6 5 si c. lim Th bst way to gt a A Gt vido solutios for this workbook at
4 Computatios with Taylor Sris Qustios: 4) Aswr th followig qustios: a. Comput / with a rror of lss tha.. b. Comput si with a rror of lss tha.. c. Comput arcta.5 with a rror of lss tha.. 5) Aswr th followig qustios: a. Evaluat usig th first thr ozro lmts of maclauri sris ad stimat th rror. b. Evaluat cos4 usig th first thr ozro lmts of maclauri sris ad stimat th rror. c. Evaluat l.5 usig th first thr ozro lmts of maclauri sris ad stimat th rror. 6) Aswr th followig qustios: a. What is th maimum rror i approimatig b. What is th maimum rror i approimatig c. What is th maimum rror i approimatig si for?! 6 l for.? cos for.?! 7) Aswr th followig qustios: a. For which valus of is si with rror lss tha.?! 5 7 b. For which valus of is arcta with rror lss tha.? 5 7 8) Aswr th followig qustios:. si a. Approimat d with a rror lss tha.. b. Approimat c. Approimat. l d with a rror lss tha...5 cos d with a rror lss tha.. Th bst way to gt a A Gt vido solutios for this workbook at 4
5 Fial Aswrs: ) )! )! 4) 5) 6) l!! 4 4 all 8)! 7) 9) sih all! l -...! ) ) ) all! )! ) 5) 5 5 6)... 7) 8) 9) si ) cos ) l 4 ) l.5 ) a. b. c. 4) a. 58 b. c ) a. 5 b. c ) a.. b..5 c. 5! 7 7) a. 5. b ) a b. 9 4 c Th bst way to gt a A Gt vido solutios for this workbook at 5
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