Page 97 - DECO403_MATHEMATICS_FOR_ECONOMISTS_HINDI

VED1
E\L-LOVELY-H\math4-1 IInd 21-10-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

bdkbZ y?kqx.kdh; vodyu

mÙkj uksV
sin x

< ; * = <

* ; =
x
1  x 

* (log log x + ) ;  + log (1 + ) x 
log x  1 + x 
8 8 ; 8 8 ; 8 8
1 − 1
# (1 + x 23/2 % (1 + ) x 3/ 2 (1 − ) x 1/ 2
)

2 + 3x − 4x − 2 3x 3

' *
*
;
+ 2(1 + x ) (1 + x 25/ 2
)

x + 2 x + 1  1 − x 2 
x
- e x x (1 + log x ) x − 2 x + 1   x + 4 x + 2 1  
x
e
(x − a ) (x − ) b  1 1 1 
x − c   x − a + x − b − 2(x − ) c   * * * 8

(x + 1) 2 x − 1  2 1 3 
10 ⋅ 10 10 x (log 10) 2 (x + 4) e x   x + 1 + 2 (x − 1) − x + 4 − 1  
x
3
e
4-2 vuUr Jsf.k;ksa dk ;ksxiQy % "

mnkgj.k 1- ;fn
x x x ...∞ rks fl¼ dhft, fd dy = y 2
dx 1 − y logx

gy % : x x x ...∞ : D;ksafd x x ...∞ :
y?kqx.kd ysus ij * : *
nksuksa i{kksa dk osQ lkis{k vodyu djus ij
1 dy . d log x + log x dy
.
y dx : y dx dx
1 dy
: y . + log x
x dx
 1  dy y
∴  − log x  =
 y  dx x
dy y 2
vr% x : bfr fl¼e~A
dx 1 − y log x
dy cos x
mnkgj.k 2- ;fn : sin x+ sin x+ sin x+ .... fl¼ dhft, fd = "
dx 2y − 1