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8/13/2019 Jee 2014 Booklet5 Hwt Differential Calculus 1
1/13
Wd`ymemo`dr Njmsscs
WEN/@dggcrcotdmj Nmjnujus - = 07 FRP/Emtfcemtdns
@MPC 1 PDEC 1 >9 Edoutcs EM\H^ 1 X [[[ /=9U PC^P NK@C 1 @N-=
X=U
^PM\P PDEC 1 CO@ PDEC 1 PDEC PMHCO1 YM\COP^ DBOMPS\C 1
Pfds tcst nkotmdos m tktmj kg =9 Klacntdvc Pypc ]ucstdkos. Cmnf
qucstdko nmrrdcs = emrh. Pfcrc ds OK OCBMPDWC emrhdob.
Nfkksc tfc nkrrcnt mjtcromtdvc. Kojy koc nfkdnc ds nkrrcnt.
=. ^tmtcecot 1 = Pfc `kemdo kg > > > x m nks , y m sdo
, tfco
>
x
x
(L)7 0
< >
x
x
(N)0 >
7 9 Edoutcs EM\H^ 1 X [[[ /=9U PC^P NK@C 1 @N-= X = >
=
= > = >9
=
x my tmo , x
x m
/ /
/ /, tfco
`y
`xds 1
(M)
= > < >=
=x x/ /(L)
< > < > < >=
> =x x/ /(@)
= > < >=
> =x x/ /
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8/13/2019 Jee 2014 Booklet5 Hwt Differential Calculus 1
4/13
Wd`ymemo`dr Njmsscs
WEN/@dggcrcotdmj Nmjnujus - = 04 FRP/Emtfcemtdns
4. Dg = >0
39 3 =jkb jkb x
.
/ tfco |x |lcjkobs tk 1
(M) =, (L) < =3
,
(N) =3 3
,
=9.= =
< = 7x
xjde x sdo
x
ds 1
(M)=
< >(L)
(N)
>
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8/13/2019 Jee 2014 Booklet5 Hwt Differential Calculus 1
5/13
Wd`ymemo`dr Njmsscs
WEN/@dggcrcotdmj Nmjnujus - = 39 FRP/Emtfcemtdns
@MPC 1 PDEC 1 >9 Edoutcs EM\H^ 1 X [[[ /=9U PC^P NK@C 1 @N-=
X>U
^PM\P PDEC 1 CO@ PDEC 1 PDEC PMHCO1 YM\COP^ DBOMPS\C 1
Pfds tcst nkotmdos m tktmj kg =9 Klacntdvc Pypc ]ucstdkos. Cmnf
qucstdko nmrrdcs = emrh. Pfcrc ds OK OCBMPDWC emrhdob.
Nfkksc tfc nkrrcnt mjtcromtdvc. Kojy koc nfkdnc ds nkrrcnt.
=. M sdobjc gkreujm tfmt bdvcs g (x) gkr mjj 9x wfcrc,
> 9 >
> > >
x , xg x
x , x
ds 1
(M) < = 0g x x x| |
(L) > 4g x x x| |
(@) > >g x x x| |
. Jct < =g x x x wfcrc X U `coktcs tfc brcmtcst
dotcbcr guontdko. Pfco, do (9,
0 6 3 ,
(N)3
(L) >0nks x sdo x
(N)>0 sdo x nks x (@) u
2. Dg = =
< 2 FRP/Emtfcemtdns
@MPC 1 PDEC 1 >9 Edoutcs EM\H^ 1 X [[[ /=9U PC^P NK@C 1 @N-=
X0U
^PM\P PDEC 1 CO@ PDEC 1 PDEC PMHCO1 YM\COP^ DBOMPS\C 1
Pfds tcst nkotmdos m tktmj kg =9 Klacntdvc Pypc ]ucstdkos. Cmnf
qucstdko nmrrdcs = emrh. Pfcrc ds OK OCBMPDWC emrhdob.
Nfkksc tfc nkrrcnt mjtcromtdvc. Kojy koc nfkdnc ds nkrrcnt.
=. Dg g(x) ds m tfrdnc dggcrcotdmljc guontdko sunf tfmt
>9
0 > > >
x h x .h, x
g x x
, x
ds nkotdoukus mtx5 >, tfcohds 1
(M) > (L) > (N) =3 (@) =3
2. Dg = = 9
,
(N)= =
0 3g x x x x ds 1
(M) , (L)==
=>
,
(N)= =
0 6 FRP/Emtfcemtdns
@MPC 1 PDEC 1 >9 Edoutcs EM\H^ 1 X [[[ /=9U PC^P NK@C 1 @N-=
X3U
^PM\P PDEC 1 CO@ PDEC 1 PDEC PMHCO1 YM\COP^ DBOMPS\C 1
Pfds tcst nkotmdos m tktmj kg =9 Klacntdvc Pypc ]ucstdkos. Cmnf
qucstdko nmrrdcs = emrh. Pfcrc ds OK OCBMPDWC emrhdob.
Nfkksc tfc nkrrcnt mjtcromtdvc. Kojy koc nfkdnc ds nkrrcnt.
Fkwcvcr, qucstdkos emrhc` wdtf '*' emy fmvc Ekrc tfmo koc
nkrrcnt kptdko.
=.
0
=
< =
0
0x
tmo xjkb
jdex
sdo x
ds 1
(M) 0 (L) =/0 (N) 9 (@) `kcs okt cxdst
*. Dg x sdo mo` >y nks tfco (N) = 1 =< (@) =< 1 =
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8/13/2019 Jee 2014 Booklet5 Hwt Differential Calculus 1
8/13
Wd`ymemo`dr Njmsscs
WEN/@dggcrcotdmj Nmjnujus - = >4 FRP/Emtfcemtdns
6. Jct >
,
(N)< =9
> >, ,
(@) Okoc kg tfcsc
>.=
=
(@) Okoc
6. Dg < = < =tx c , y tmo t , tfco
`y
`x
(M)
2 FRP/Emtfcemtdns
@MPC 1 PDEC 1 >9 Edoutcs EM\H^ 1 X [[[ /=9U PC^P NK@C 1 @N-=
X6U
^PM\P PDEC 1 CO@ PDEC 1 PDEC PMHCO1 YM\COP^ DBOMPS\C 1
Pfds tcst nkotmdos m tktmj kg =9 Klacntdvc Pypc ]ucstdkos. Cmnf
qucstdko nmrrdcs = emrh. Pfcrc ds OK OCBMPDWC emrhdob.
Nfkksc tfc nkrrcnt mjtcromtdvc. Kojy koc nfkdnc ds nkrrcnt.
Fkwcvcr, qucstdkos emrhc` wdtf '*' emy fmvc Ekrc tfmo koc
nkrrcnt kptdko.
=.
9
= < = 2 FRP/Emtfcemtdns
@MPC 1 PDEC 1 >9 Edoutcs EM\H^ 1 X [[[ /=9U PC^P NK@C 1 @N-=
X4U
^PM\P PDEC 1 CO@ PDEC 1 PDEC PMHCO1 YM\COP^ DBOMPS\C 1
Pfds tcst nkotmdos m tktmj kg =9 Klacntdvc Pypc ]ucstdkos. Cmnf
qucstdko nmrrdcs = emrh. Pfcrc ds OK OCBMPDWC emrhdob.
Nfkksc tfc nkrrcnt mjtcromtdvc. Kojy koc nfkdnc ds nkrrcnt.
Fkwcvcr, qucstdkos emrhc` wdtf '*' emy fmvc Ekrc tfmo koc
nkrrcnt kptdko.
=. Jct g x lc nkotdoukus mt x 5 9 mo` 9g h .
Pfc vmjuc kg
< 0
x
g x g x g xjde
x
ds 1
(M) h (L) h (@) Okoc kg tfcsc
. Dg =y xx y , tfco`y/`xds 1
(M)
y y x jkb y
x y jkb x x
(L)
y x y jkb x
x y jkb x y
(N)
y y x jkb y
x x y jkb x
(@) Okoc kg tfcsc
0. Dg= =
x t , y tt t
, tfco`y/`xds cqumj tk 1
(M)
