Page 99 - 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

nksuksa i{kksa dk y?kqx.kd ysus ij uksV
* : *

iqu% nksuksa i{kksa dk y?kqx.kd ysus ij
* * : * ; * *
nksuksa i{kksa dk osQ lkis{k vodyu djus ij

1 . 1 dy 1 dy
log y ydx : y . x + dx (log ) + x 0

 1  dy y  1 − y log . log y  x dy y
∴  log x  : ⇒   =
 y log y  dx x  y log y  dx x

dy y 2 log y
∴ : bfr fl¼e~A
dx x (1 − y log . log ) y
x
Lo&ewY;kadu

1- fjDr LFkkuksa dh iwfrZ djsa
/
B
µ
,sls iQyu ftudk vodyu y?kqx.kd ysdj Kkr fd;k tkrk gS mls --------- vodyu dgrs gSaA

 m 
log   = logm − ........
 n 

n
m
log ( ) ........ log m
: * 7 ; * #
 25 
log   = log 25 − log ........
 12 

iz'ukoyh 710

y?kq mÙkjh; iz'u
dy
1- ;fn
x + x + x + .... ∞ rks fl¼ dhft, fd (2y − 1) dx :

dy

2- ;fn
tan x + tan x + tan x + .... ∞ rks fl¼ dhft, fd (2y − 1) :
dx

x ....∞ dy y 2
3- ;fn
x x rks fl¼ dhft, fd x dx = 2 − y log x

x
x
4- ;fn
(sin )x (sin ) (sin )....∞ rks fl¼ dhft, fd dy = y 2 cot x
dx 1 − y log (sin ) x