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    27-Jun-2015
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Επιλεγμένες ασκήσεις από το ανανεωμένο βιβλίο του φίλου Γιώργου Μαυρίδη, για την Γ΄ Λυκείου. Το βιβλίο ξεχωρίζει για τις πολλές λυμένες ασκήσεις που περιέχει, στις οποίες ο μαθητής θα βρει πολλά και εξόχως ενδιαφέροντα θέματα.

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  • 1. 9 786188 021495 ISBN: 978-618-80214-9-5

2. . 3. 4. 2013 5. ........................................................................................ 11 ........................................................................................ 13 .............................................................................. 113 .......................................................................................... 141 ....................................................................... 151 ........................................................................................ 153 .............................................................................. 347 .......................................................................................... 391 ............................................................... 401 ........................................................................................ 403 .............................................................................. 477 .......................................................................................... 501 .................................................................................................... 507 ................................................................................................ 569 6. ............................................................... 11 ........................................................................................ 13 .............................................................................. 259 .......................................................................................... 317 ........................................................................... 329 ........................................................................................ 331 .............................................................................. 505 .......................................................................................... 543 ................................................................................ 555 .................................................................................................... 575 ................................................................................................ 636 7. 243 f : x : i) h 0 lim f x 2h 2f x h f x 0 ii) h 0 f x 2h f x h lim f x h iii) 2h 0 f x 2h 2f x h f x h i) H f h 0 ii) h 0 h 0 f x 2h f x h f x 2h f x f x h f x lim lim h h h h 0 h 0 f x 2h f x f x h f x 2lim lim 2h h 2f x f x f x iii) E De l Hospital 0 0 2h 0 h 0 2 f x 2h 2f x h f xf x 2h 2f x h f x lim lim h h h 0 2f x 2h 2f x h lim 2h h 0 f x 2h f x h lim h ii) f x 8. 244 f : g : g x f x 2x y 2x fC x lim f x i) g ii) x lim f x x lim g x 0 iii) g x 0 x iv) fC i) g x f x 2 f f 1 2 1 2 1 2 1 2 1 2 f x f x f x 2 f x 2 g x g x g g ii) y 2x fC x x x lim f x lim f x 2x 2x x g g 9. x f x lim x x De L Hospital x x x f x f x lim lim lim f x x x x 2 lim f x x x x x iii) g x x x g x 0 x iv) iii) g fC x x g x x x g x 0 f x 2x 0 x f x 2x x fC 10. 246 1 1 xf x x , x 0, 1 1, g x x g x g 1 0 i) N ii) N g iii) N f iv) f x i) g 1 0 1 g x g 1 g 2 g x x x x Fermat 2 g 1 0 0 1 1 g 1 0 g x 1 Fermat 11. 247 ii) g i 1 x 2 2 1 x 1 1 x x x 1 x 2 x 1 x 2 x 1 x 2 x 1 x g g x 1 iii) 1 1 x f x x 0 1 1 x 1 x 1 x f x e e e x 0 1 g g 0 12. 248 1 x 1 x 1 1 x 1 1 x 1 1 x 1 1 x 2 2 2 2 f x e e 1 x x 1 x 1 xx 1 x 1 xx 1 x g x x 1 x i) g x 1 g x g 1 0 1 1 x 2 g x f x x 0 1 x f iv) iii) f x 0 xx 1 x 1 x 0 x 01 x 1 x x 0 1 lim 1 1 x x 0 f 13. 249 u 1 x u1 x x 0 x 0 u 0 0 1 xlim lim lim lim 1 1 x 1 x1 x u 1 x u 11 x x 1 x 1 u 1 1 e 1 xlim lim lim lim 0 1 x 1 x1 x u 1 x u 01 x x x u 0 x 0 x 1 1 e xx 1 1 e f x 1 1 e e 1 e x y y 1 y O 1 1 e 14. 3 4 3 2 i) f ii) iii) N f i) 3 4 3 2 2 3 3 2 2 3 2 1 x 2 3 2 2 2 2 1 x 2 1 x x 0 f f f 15. ii) f x x 0 2 x x 2 x lim x 72 36 x x 2 x lim x x x x x lim 72 36 72 lim 36 lim x x x x 72 lim 36 0 x 1 72 lim 36 x 2 x 0 x 0 2 x 0 x 0 2 x 0 x 0 2 x 0 72lim 36 0 2 1 x 72lim 0 2 1 x 1 x72lim 2 1 x f x 0 limf x x x 16. iii) ii) f 0 0 f 0f x f x 0 0 0f x f x 0 0 f 0 0 f 0x 0 0 f f x 0 0x f f 0 17. 2 i) f ii) N f iii) N f iv) x i) 2 1 x x 0 2 2x 2 2 x x 2x 2 x x 02x 2 x x 02x 2 x f f x 0 1 f f 0 18. f fC ii) i) f f x 1 f x f 1 0 f ii) f 2 x 0 x 0 2 2 x 0 x 0 x 0 2 1 x 1 2 xlim lim lim 2x 0 1 1 x x 2 x x 2 x lim x 1 2 x 2 x lim x f f f f f f 19. x x x lim 1 2 1 2 lim x x 1 2 lim x 1 1 2 lim x x 0 x iv) H x x 0 2 2 2 f x (1) f 1 1 (1) f x fC y fC x y fC y O 1 1 20. f : 1, f e 1 2 f xf x x 4 4x f xf x x 1 i) 2 ii) N fC iii) f iv) f f i) 2 x f x f x 4 f x f x 4xf x f x x 1 222 x f x 4 f x 4xf x f x 0 x 1 22 xf x 2 f x 2 xf x 2 f x 0 x 1 2 xf x 2 f x 0 x 1 xf x 2 f x 0 x 1 xf x 2 f x x 1 f x 1 x2 f x x 1 x 1 x 1 21. x e x 1 2 ii) 2 x x 0 0 0 0 0 0 0 00 f x f x 0 x 0 0 0x f x f x 0 20 0 0 0 2 0 0 0 0 0 0 0 2 0 x 22 2 2 0 2 2 0 2 2 2 e e e 2 2 4 y 4 x e e 2 2 4 4 e e 0 0 22. iii) x f fC x 1 x 1 x 1 fC fC 1 2 x x 1 xx y 0 x x fC fC iv) 2 2 2 f x f x 2 2 2 x x x 1 x2 2 x x x x 1 x x 1 x f fC x 1 e f f 0