Page 49 - 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

bdkbZ lhek o lrrrk

 2 − + 2ax a 2  x uksV
mnkgj.k 3- lim   dk eku Kkr dhft,A
xa  x − a 

 2 − + 2ax a 2  x 2 (x − ) a 2
gy % lim   : lim
x →a  x − a  x → a x − a
: lim 8
:
8
: - mÙkj
x → a
x
x 2 − 3+ 2
mnkgj.k 4- lim dk eku Kkr dhft,A
x 2 x 2 + x − 6
x − 2 3x + 2 (x − 2) (x − 1) (x − 1)
gy % lim : lim : lim < ≠ =
x → 2 x + 2 x − 6 x → 2 (x − 2) (x + 3) x → 2 (x + 3)

21 1
−
: : mÙkj
2 + 3 5
fLFkfr 3 3 ) % vifjes; iQyu dh lhek 3 ,

;fn : vkSj ,d vifjes; iQyu gS rks dh lhek Kkr djus osQ fy, igys iQyu dks ifjes; cuk
yhft, fiQj fLFkfr dh rjg lhek Kkr dj yhft,A
3 1+ x − 1
mnkgj.k 5- lim dk eku Kkr dhft,A
x 0 x
1
3 1 + x − 1 (1 + ) x 3 − 1
gy% lim : lim
x → 0 x x → 0 x
11 − 1 


1 33  

1 + x + x + 2 ......∞ − 1
: lim 3 2!
x → 0 x
1  − 2  x
1 3   3   1 1
: lim + + ...... ∞ : + 0 = mÙkj
x → 0 3 2! 3 3

(1 + 1/2 − ) x − (1 ) x 1/2
mnkgj.k 6- fl¼ dhft, % lim
"
x 0 x

(1 + ) x 1/ 2 − (1 − ) x 1 / 2 1 + x − 1 − x
gy% lim : lim
x → 0 x x → 0 x
1 + x − 1 − x 1 + x + 1 − x
: lim ×
x → 0 x 1 + x + 1 − x

(1 + ) x − (1 − ) x 2x
: lim : lim
x → 0 x (1 + x + 1 − x ) x → 0 x (1 + x + 1 − x )