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DifferentiationB. Com.
III year
Advance Business Mathematics
8584992992
Session
2016 - 17
Total Solution :Total Problems :
8584992992
DifferentiationB. Com.
III year
Advance Business Mathematics
8584992992
Session
2016 - 17
Total Solution :Total Problems : Exercise [4A]
8584992992
DifferentiationB. Com.
III year
Advance Business Mathematics
8584992992
Session
2016 - 17
 
 
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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
DifferentiationB. Com.
III year
Advance Business Mathematics
8584992992
Session
2016 - 17
 
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Answers[C.U. B. Com. (Hons.) ’91]
4A : Section - A
DifferentiationB. Com.
III year
Advance Business Mathematics
8584992992
Session
2016 - 17
 
 
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Answers



x
x
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4A : Section - A
DifferentiationB. Com.
III year
Advance Business Mathematics
8584992992
Session
2016 - 17
32
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[C.U. B. Com. (Hons.) ’82]
4A : Section - B
DifferentiationB. Com.
III year
Advance Business Mathematics
8584992992
Session
2016 - 17
a
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Answers
4A : Section - B
DifferentiationB. Com.
III year
Advance Business Mathematics
8584992992
Session
2016 - 17
)log(5xi)(
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2
12
2
2
2
9
Answers
xxxx
x
x
xe
x
x
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[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
DifferentiationB. Com.
III year
Advance Business Mathematics
8584992992
Session
2016 - 17
ca
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Answers
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[C.U. B. Com. (Hons.) ’87]
4A : Section - B
DifferentiationB. Com.
III year
Advance Business Mathematics
8584992992
Session
2016 - 17
   
   
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4A : Section - B
DifferentiationB. Com.
III year
Advance Business Mathematics
8584992992
Session
2016 - 17
 
   
    724214Fii
596i
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
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
 
xx
xx
x
xnnx nn
4A : Section - B
DifferentiationB. 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 .
DifferentiationB. Com.
III year
Advance Business Mathematics
8584992992
Session
2016 - 17
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DifferentiationB. Com.
III year
Advance Business Mathematics
8584992992
Session
2016 - 17

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

  • 1. DifferentiationB. Com. III year Advance Business Mathematics 8584992992 Session 2016 - 17 Total Solution :Total Problems : 8584992992
  • 2. DifferentiationB. Com. III year Advance Business Mathematics 8584992992 Session 2016 - 17 Total Solution :Total Problems : Exercise [4A] 8584992992
  • 3. DifferentiationB. Com. III year Advance Business Mathematics 8584992992 Session 2016 - 17                 x x x e xx x x xx x x xf x xxxf af axxfy xx xxfy x y xx yyxxfy x x 3log(x) (ix) (viii) (vii) 0(vi) 52(v) 32(iv) 2(iii) 0 1 (ii) (i) :functionsfollowingtheofsderivativetheprinciplefirstthefromFind5. .0atabledifferentinotisfunctionthat theShow.4 ?exist'doesWhen .atfunctiontheofderivativehandleftandderivativehandrighttheDefine3. 0.0001.and0at functionfor theratioincrementthefindAlso.ofincrementanto ingcorrespondofincrementthefind;offunctionvalued-singleabeLet2. ).2(ofderivativethefindtodefinitionthisuseandfunctionaofderivativetheDefine.1 3 6 3 3 2 2 2 3               x x xe x x xx x x xfxxfy x 1 (x) 3 1 (ix) 6(viii)3(vii) 2 1 (vi)6(v) 4(iv)22(iii) 2 (ii)3(i).5 100);()(.2 2.1 3 2 53 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
  • 4. DifferentiationB. Com. III year Advance Business Mathematics 8584992992 Session 2016 - 17                                   ....derivativedenotesdasherewh ''' that,prove,andoffunctionsabledifferentitwoareandIf.8 .'lim that,show,'beatofderivativetheIf7. 9.at 1 viii .2atevii . 27 1 atvi .2atv .1at0 1 iv .0at 32 1 iii 3.at4ii 1.at4i :oftscoefficienaldifferentithedefinitionfromFind6. 2/| 3 2 3 xtrw u u u u y y uvyxvu aafaf ax xafaxf afaxxf x x x xxxf xx xx x xxf x x xy xx ax x                 54 1 (viii) 2 1 (vii) 2vi)( 22 1 (v) 0(iv) 9 2 (iii) 0(ii) 3(i).6   e Answers[C.U. B. Com. (Hons.) ’91] 4A : Section - A
  • 5. DifferentiationB. Com. III year Advance Business Mathematics 8584992992 Session 2016 - 17                   .1at12ofabilitiydifferentiandcontinuitytheExamine12. .1atderivativethefindHence,.1atabledifferentiisthatshownthe 1for 2 1 1for 32 34 If.11 .3atofabilitydifferentitheexamineHence . 3 3 limand 3 3 limevaluate2,3If.10 .1atofabilitydifferentiandcontinuitytheDiscuss .1when34 10henw45 Let,.9 2 2 33x 2                            xxxxf xxy x x xx xx y xxf x fxf x fxf xxf xxf xxx xx xf x .1atabledifferentinotbutContinuity.11 3atabledifferentinot;(-1)and1.10 1atabledifferentiandContinuous.9 Answers    x x x 4A : Section - A
  • 6. DifferentiationB. Com. III year Advance Business Mathematics 8584992992 Session 2016 - 17 32 24 2 2 22 32 4 2 3 7 16 543 2(xi) 2 43 (x) )1()2(ix)( 432 (viii) )2((vii) 5 5 1 )vi( 2 36 2(v) 32 )iv( 2 1 )iii( 3)ii( )i( :funtionsfollowingtheateDifferenti.1 xxx x xx xxx x xx 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
  • 7. DifferentiationB. Com. III year Advance Business Mathematics 8584992992 Session 2016 - 17 a a xxx x xx xxm x xxeey xxy xey emxy xy exxy dx dy loglog5vi)( 1010log(v) 2log32(iv) 432(iii) log(ii) 24log3(i) whenFind.2 log11 10 10 12 2         x a e x ex xe x x e emmmx e x ex x ae xx e x x e x x e xm x          log 1 15log5(vi) 1010log10log 1 (v) 3 2log2(iv) 4log32(iii) log 1 (ii) 22 3 (i).2 11 9 10 12 1 2 2 1 Answers 4A : Section - B
  • 8. DifferentiationB. Com. III year Advance Business Mathematics 8584992992 Session 2016 - 17 )log(5xi)( log 2 (x) (ix) log322viii)( 5vii)( )25)((2(vi) log2(v) )1((iv) log(iii) log(ii) 10(i) :functionsfollowingtheateDifferenti.3 3 3 2 2 3 10 xx x xx xx xx xx xx x x x exx x e x ee ee x xex ex xx x ex xx xx x xw.r.t.                                     5log1log15(xi) 1 2loglog12(x) 21(ix) log 1 32log32(viii) 5log121 2 5 (vii) 2532(vi) 2loglog 1 2(v) 1(iv) log1 2 1 (iii) log31(ii) 10log1010(i).3 2 12 2 2 2 9 Answers xxxx x x xe x x exx x x e xx x x ex x x xx xx x x x xx xx 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
  • 9. DifferentiationB. Com. III year Advance Business Mathematics 8584992992 Session 2016 - 17 ca cb bc ba ab ac cbcabcbaacab x x x xxxy xxxxxx y dx dy xx xx x x e x x x x x                                                1 1 1 1 1 1 2 2 ii)( 1 1 1 1 1 1 (i) when0thatshowcasesfollowingofeachIn.5 1 1 (vi) 110 (v) 2 log iv)( 1 (iii) 1 1 (ii) 1 1 (i) :functionsfollowingtheofsderivativetheFind.4   22 2 2 2 2 2 )1( )1(2 (vi) 1)110log(10 1 (v) )2loglog 1 ( 2 1 (iv) )1( 1)1( (iii) )1( 1 (ii) )1( 2 (i).4 Answers xx x x x x x e xe xx x x x x x          [C.U. B. Com. (Hons.) ’87] 4A : Section - B
  • 10. DifferentiationB. Com. III year Advance Business Mathematics 8584992992 Session 2016 - 17                       ?exsitent-nonis'for whichofany value thereIs.0'for whichofvaluesthealsoFind.'find, 14 If.15 .,thatshow,... !4!3!2 1If.14 .2'find, 4 42 2If.13 .22that,show 1 If.12 .01,thatprove 4 If.11 .05,thatshowIf.10 .2'ofvaluethefind,2432If.9 .ofvaluethefind,If.8 .find,02'and542If7. 0.for whichofvaluesthefind,73632If6. 2 432 5 23 1 2 23 23 xfx xfxxf x x xf y dx dyxxx xy f x x x xxf xy dx dy x x xy yy dx dy x x x y y dx dy xxy fxxxxf dt ds cbtats pfxpxxxf dx dy xxxxy t                      4 1 ; 2 1 ,0; )14( )12(2 .15 4 3 213. 40.9 2.8 1.7 3and2.6 2 Answers       xxx x xx ba p xx 4A : Section - B
  • 11. DifferentiationB. Com. III year Advance Business Mathematics 8584992992 Session 2016 - 17           724214Fii 596i :functionsfollowingtheofpointsstationarytheFind17. .1...321 seriesofsumthefind, 1 -1 ...1relationtheFrom16. 23 23 22 12        xxxx xxxxf xnxx x x xxx n n n 2 1 and4(ii) 3and1i)(.17 )1( )1(1 .16 2 1 Answers      xx xx x xnnx nn 4A : Section - B
  • 12. DifferentiationB. 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 .
  • 13. DifferentiationB. Com. III year Advance Business Mathematics 8584992992 Session 2016 - 17 For Download Links www.eblackboard.co.in www.facebook.com/eblackboard www.slideshare.net/eblackboard www.youtube.com/eblackboard
  • 14. DifferentiationB. Com. III year Advance Business Mathematics 8584992992 Session 2016 - 17