# Exercise 4A - Differentiation Problems [B. Com. 3rd year - S. N. De]

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This set is prepared on the basis of Advanced Business Mathematics - S. N. De. for B. Com. III year students [ CU ] .

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Differentiation B. Com. III year Advance Business Mathematics 8584992992 Session 2016 - 17 Total Solution : Total Problems : 8584992992

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Differentiation B. Com. III year Advance Business Mathematics 8584992992 Session 2016 - 17 Total Solution : Total Problems : Exercise 4A 8584992992

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Differentiation B. Com. III year Advance Business Mathematics 8584992992 Session 2016 - 17                 x x x e x x x x x x x x x f x x x x f a f a x x f y x x x x f y x y x x y y x x f y x x 3 log x ix viii vii 0 vi 5 2 v 3 2 iv 2 iii 0 1 ii i : functions following the of s derivative the principle first the from Find 5. . 0 at able differenti not is function that the Show . 4 exist does When . at function the of derivative hand left and derivative hand right the Define 3. 0.0001. and 0 at function for the ratio increment the find Also . of increment an to ing correspond of increment the find of function valued - single a be Let 2. . 2 of derivative the find to definition this use and function a of derivative the Define . 1 3 6 3 3 2 2 2 3                      x x x e x x x x x x x f x x f y x 1 x 3 1 ix 6 viii 3 vii 2 1 vi 6 v 4 iv 2 2 iii 2 ii 3 i . 5 100 . 2 2 . 1 3 2 5 3 2 3 2          Answers C.U. B. Com. Hons. ’81 C.U. B. Com. Hons. ’85 C.U. B. Com. Hons. ’83 C.U. B. Com. Hons. ’87 C.U. B. Com. Hons. ’88 C.U. B. Com. Hons. ’82 C.U. B. Com. Hons. ’04 4A : Section - A

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Differentiation B. Com. III year Advance Business Mathematics 8584992992 Session 2016 - 17                                   . . . . derivative denotes dash ere wh that prove and of functions able differenti two are and If . 8 . lim that show be at of derivative the If 7. 9. at 1 viii . 2 at e vii . 27 1 at vi . 2 at v . 1 at 0 1 iv . 0 at 3 2 1 iii 3. at 4 ii 1. at 4 i : of ts coefficien al differenti the definition from Find 6. 2 / | 3 2 3 x t r w u u u u y y uv y x v u a af a f a x x af a xf a f a x x f x x x x x x f x x x x x x x f x x x y x x a x x                          54 1 viii 2 1 vii 2 vi 2 2 1 v 0 iv 9 2 iii 0 ii 3 i . 6   e Answers C.U. B. Com. Hons. ’91 4A : Section - A

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Differentiation B. Com. III year Advance Business Mathematics 8584992992 Session 2016 - 17                   . 1 at 1 2 of abilitiy differenti and continuity the Examine 12. . 1 at derivative the find Hence . 1 at able differenti is that show n the 1 for 2 1 1 for 3 2 3 4 If . 11 . 3 at of ability differenti the examine Hence . 3 3 lim and 3 3 lim evaluate 2 3 If . 10 . 1 at of ability differenti and continuity the Discuss . 1 when 3 4 1 0 hen w 4 5 Let . 9 2 2 3 3 x 2                                            x x x x f x x y x x x x x x y x x f x f x f x f x f x x f x x f x x x x x x f x . 1 at able differenti not but Continuity . 11 3 at able differenti not -1 and 1 . 10 1 at able differenti and Continuous . 9 Answers    x x x 4A : Section - A

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Differentiation B. Com. III year Advance Business Mathematics 8584992992 Session 2016 - 17 3 2 2 4 2 2 2 2 3 2 4 2 3 7 16 5 4 3 2 xi 2 4 3 x 1 2 ix 4 3 2 viii 2 vii 5 5 1 vi 2 3 6 2 v 3 2 iv 2 1 iii 3 ii i : funtions following the ate Differenti . 1 x x x x x x x x x x x x x x x x x x x x x x x x x w.r.t. x                  C.U. B. Com. Hons. ’82 4A : Section - B

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Differentiation B. Com. III year Advance Business Mathematics 8584992992 Session 2016 - 17 a a x x x x x x x x m x x x e e y x x y x e y e m x y x y e x x y dx dy log log 5 vi 10 10 log v 2 log 3 2 iv 4 3 2 iii log ii 2 4 log 3 i when Find . 2 log 1 1 10 10 1 2 2                        x a e x ex x e x x e e m m mx e x e x x a e x x e x x e x x e x m x                    log 1 1 5 log 5 vi 10 10 log 10 log 1 v 3 2 log 2 iv 4 log 3 2 iii log 1 ii 2 2 3 i . 2 1 1 9 10 1 2 1 2 2 1 Answers 4A : Section - B

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Differentiation B. Com. III year Advance Business Mathematics 8584992992 Session 2016 - 17 log 5 xi log 2 x ix log 3 2 2 viii 5 vii 2 5 2 vi log 2 v 1 iv log iii log ii 10 i : functions following the ate Differenti . 3 3 3 2 2 3 10 x x x x x x x x x x x x x x x x e x x x e x e e e e x x e x e x x x x e x x x x x x x w.r.t.                                             5 log 1 log 1 5 xi 1 2 log log 1 2 x 2 1 ix log 1 3 2 log 3 2 viii 5 log 1 2 1 2 5 vii 2 5 3 2 vi 2 log log 1 2 v 1 iv log 1 2 1 iii log 3 1 ii 10 log 10 10 i . 3 2 1 2 2 2 2 9 Answers x x x x x x x e x x e x x x x e x x x x e x x x x x x x x x x x x x x x x e x                                        C.U. B. Com. Hons. ’86 N.B.U. B. Com. ’05 C.U. B. Com. Hons. ’87 C.U. B. Com. Hons. ’85 4A : Section - B

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Differentiation B. Com. III year Advance Business Mathematics 8584992992 Session 2016 - 17 c a c b b c b a a b a c c b c a b c b a a c a b x x x x x x y x x x x x x y dx dy x x x x x x e x x x x x                                                            1 1 1 1 1 1 2 2 ii 1 1 1 1 1 1 i when 0 that show cases following of each In . 5 1 1 vi 1 10 v 2 log iv 1 iii 1 1 ii 1 1 i : functions following the of s derivative the Find . 4   2 2 2 2 2 2 2 1 1 2 vi 1 1 10 log 10 1 v 2 log log 1 2 1 iv 1 1 1 iii 1 1 ii 1 2 i . 4 Answers x x x x x x x e x e x x x x x x x              C.U. B. Com. Hons. ’87 4A : Section - B

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Differentiation B. Com. III year Advance Business Mathematics 8584992992 Session 2016 - 17                       exsitent - non is for which of any value there Is . 0 for which of values the also Find . find 1 4 If . 15 . that show ... 4 3 2 1 If . 14 . 2 find 4 4 2 2 If . 13 . 2 2 that show 1 If . 12 . 0 1 that prove 4 If . 11 . 0 5 that show If . 10 . 2 of value the find 2 4 3 2 If . 9 . of value the find If . 8 . find 0 2 and 5 4 2 If 7. 0. for which of values the find 7 36 3 2 If 6. 2 4 3 2 5 2 3 1 2 2 3 2 3 x f x x f x x f x x x f y dx dy x x x x y f x x x x x f x y dx dy x x x y y y dx dy x x x y y dx dy x x y f x x x x f dt ds c bt at s p f x px x x f dx dy x x x x y t                                                      4 1 2 1 0 1 4 1 2 2 . 15 4 3 2 13. 40 . 9 2 . 8 1 . 7 3 and 2 . 6 2 Answers             x x x x x x b a p x x 4A : Section - B

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Differentiation B. Com. III year Advance Business Mathematics 8584992992 Session 2016 - 17           7 24 21 4 F ii 5 9 6 i : functions following the of points stationary the Find 17. . 1 ... 3 2 1 series of sum the find 1 - 1 ... 1 relation the From 16. 2 3 2 3 2 2 1 2                      x x x x x x x x f x n x x x x x x x n n n 2 1 and 4 ii 3 and 1 i . 17 1 1 1 . 16 2 1 Answers           x x x x x x n nx n n 4A : Section - B

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Differentiation B. Com. III year Advance Business Mathematics 8584992992 Session 2016 - 17 The solutions of this set of exercise will be published soon. Additional set of illustrations and problems will be Published shortly. Any error if found please Whatsapp 8584992992 for instantly correction .