Page 50 - DECO403_MATHEMATICS_FOR_ECONOMISTS_HINDI

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

vFkZ'kkfL=k;ksa dk xf.kr

uksV 2 2
: lim = : mÙkj
+
x → 0 1 + x + 1 − x 11
fLFkfr ' 3 ' % iQyu dh lhek Kkr djuk] tc → ∞
1
,sls iQyuksa esa igys : j[kdj lhek dk :i → ∞ dks cnydj 3 → - osQ :i esa j[k nhft,A fiQj fLFkfr
Z
dh Hkk¡fr lhek fudky yhft,A
x
9x 2 + 3 + 7
mnkgj.k 7- lim dk eku Kkr dhft,A
x ∞ 5x 2 + 2 + 1
x
∞
gy % Li"V gS fd ;fn : ∞ j[kk tk, rks va'k vkSj gj gks tk;sxhA blfy, va'k vkSj gj nksuksa esa
∞
dk Hkkx nsus ij
3 7
9x + 2 3x + 7 9 + + 2 9 + 0 + 0
lim : lim x x =
x →∞ 5x + 2 2x + 1 x →∞ 2 1 5 + 0 + 0
5 + +
x x 2
9
: 9 tcfd → ∞
5
3 7 2 1 9
pw¡fd → ∞ blfy, , , , 2 'kwU; dh vksj vxzlj gksaxs rFkk iQyu dh vksj vxzlj gksrk gSA
x x 2 5x x 5

9x + 2 3x + 7 9
lim
vr% 2 : mÙkj
x →∞ 5x + 2x + 1 5
x m − a m
mnkgj.k 8- fl¼ dhft, fd lim = ma m − 1 tgk¡ dksbZ ifjes; la[;k gSA
x x − a

x m − a m
gy % izFke fof/ % ck;k¡ i{k : lim
x → a x − a
(x − a ) (x m − 1 + x m − 2 a + x m − 3 a + 2 .... + a m − 1 )
: lim
x → a (x − ) a

: lim (x m − 1 + x m − 2 a + x m − 3 a + 2 .... + a m − 1 ) 9 tc ≠
x → a
: a m − 1 + a m − 1 + .... + a m − 1 : ma m − 1 : nk;k¡ i{kA

x m − a m
lim ,
f}rh; fof/ % x → a x − a :
; , j[kus ij vkSj tc →
, → -

a m  1 + h  m − a m
(a + ) h m − a m   a  
: lim : lim
h→ 0 (a + ) h − a h→ 0 h