Page 45 - DECO403_MATHEMATICS_FOR_ECONOMISTS_PUNJABI

VED1
E L-LOVELY-H math2-1 IInd 21-10-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

fJekJh^2 L ;hwk ns/ brkskosk

f () x B'N
i/eo y= f x = , sK ;hwk gsk eoB d/ bJh j/mbhnK uko soQK dhnK ;fEshnK j'DrhnKL
()
y () x
0
;fEsh 1 (Type 1)L id'A x fi a i/eo ()af = 0 , y () = sK () = fijVk nfBoXko:
a
0
fa
0
j?. fJ; soQK d/ cbB dh ;hwk j/m nB[;ko gsk ehsh ik ;edh j?^
() cbB B{z jZb eoe/ ns/ x „ a wzB e/ nzP ns/ jo Bkb T[G/fBPm r[Dbyzv B{z eZN fdU.
i
() pkeh yzvK ftZu x d/ ;EkB a oZy e/ wkB gsk eo fbU. fJjh cbB dh x fi a T[Zs/ ;hwk
ii
j't/rh.
;fEsh 2 (Type 2)L x fi a T[Zs/ () dh ;hwk gsk eoB d/ bJh x = a+h oZye/, fJZE/ h
fx
XBkswe iK foDkswe tkXk (Increment) j? f ( )a+h dh ;hwk gsk eo'. id'A h fi 0 Gkt
0
( ) f a+h ftZu h = oZye/ cbB dk wkB gsk eo fbU. fJjh cbB dh x fi a T[Zs/ ;hwk j't/rh
feT[Afe id'A
x = a+h ns/ x fi a sK h fi 0 H
;t?^w[bKeD (Self Assessment)

1H ykbh ;EkBK dh g{osh eo' (Fill in the blanks)^
(i) i/eo fJZe ;zfynk A d/ tZb/ gqtfos j[zd/ jB sK sK fJ; ;zfynk A B{z cbB f (x) dk x = a
T[Zs/ HHHHHHHHHHHHHHH efjzd/ jB.
(ii) id'A cbB dh ;hwk ;[szso uo d/ wkB d/ yZp/ gk;/ s'A gqgks ehsh iKdh j? sK T[;B{z HHHHHHHHHH
efjzd/ jB.
(iii) i/eo fe;h cbB f(x) dh x = a T[Zs/ dZyD ns/ tkw gZy d'B'A ;hwktK ftdwkB ns/ fJZe ;wkB
j'D, sK cbB f(x) dh x = a T[Zs/ ;hwk dk HHHHHHHHHHHH j[zdk j?.
(iv) uo x d/ fe;h wkB a d/ bJh cbB f (x) dk wkB ns/ HHHHHHHHHHHHH wkB fGzB j'Dk io{oh BjhA
j?.
(v) Gkt/A fe ;kB{z ;hwk gsk eoB d/ bJh dZyD gZy ns/ tkw gZy d'B'A ;hwktK gsk eoBhnK
ukjhdhnK jB gozs{ HHHHHHHHHHHHHH ;so s/ n;hA ;hwk finkdkso f;ZX/ jh gsk eod/ jK.

jZb ;fjs T[dkjoD

edh^edh T[GfBPm r[Dbyzv Bkb Gkr d/Dk ;ob BjhA j[zdk j?. nfijh ;fEsh ftZu (ii) ftXh dk
T[g:'r eoe/ ;hwk ;obsk Bkb ikDh ;edh j?. fBwB T[dkjoDK s'A fefonk ;gPN j' ikt/rh.
fNZgDh^nzP ns/ jo d'jK B{z T[;d/ T[GfBPm r[Dbyzv fijVk Iho' BjhA, Bkb Gkr d/Dk s[ozs ;zGt
Bk j't/ sK Pq/Dh gq;ko (expansion in series) iK fe;h o{gKsoD (transformation) d/ pknd fJj
fefonk ;zGt j' ;edh j?.
x 3 - a 3
T[dkjoD 1H lim dk wkB gsk eo'.
-
x fi a xa

LOVELY PROFESSIONAL UNIVERSITY 39