Page 261 - DECO403_MATHEMATICS_FOR_ECONOMISTS_PUNJABI

VED1
E L-LOVELY-H math16-1 IInd 21-10-11 IIIrd 21-4-12 IVth 20-8-12 Vth 20-8-12 Vth 10-9-12

fJekJh^16 L nB[ebB d/ nkofEe gq:'r

7H e[ZbQ bkrs cbB f (x) gsk eo' i/eo x & e[ZbQ T[sgkdB B'N
3
(i) 3x – 4x + 5, x = 0 T[Zs/ 100 o[L e[ZbQ bkrs
100
(ii) , x = 0 T[Zs/ 100 o[L e[ZbQ bkrs
x
(iii) 6.75 – 0.0006x, x = 0 T[Zs/ 10,485 o[L e[ZbQ bkrs.
8H Gsk eo'L

(i) 1 ∫ 5 x x dx (ii) 1 ∫ 14 x dx
3
+
)e +
+
x
(iii) 1 ∫ 3 (1 5x x 3 ) dx (iv) 1 ∫ 3 ( 2x e dx
2
9H i/eo wzr cbB teo p = 33 – 3x – 2x j't/ ns/ x = 3 fJekJh j't/ sK T[gG'esk pus
gsk eo'.
3
10H wzr cbB p = 100 – 2x j't/ sK p = 5 o[L T[Zs/ T[gG'esk pus fezBh j't/rh< i/eo p = 0
j't/ sK pus fezBh j't/rh<

;t?^w[bKeD (Self Assessment)

2H pj[ftebgh gqPB (Multiple Choice Questions)^
4H e[ZbQ bkrs & HHHHHHHHHHHHH <

(a) ∫ ;hwKs bkrs (b) ∫ g{oD bkrs (c) ∫ e[ZbQ bkrs (d) ∫ jkBh
5H T[gG'esk pus B{z fe; ftXh d[nkok gsk ehsk ik ;edk j?<

(a) fBy/VB (b) fBy/Ve
(c) nB[ebB (d) eq/wo
6H ;hwKs bkrs & HHHHHHHHHHHH j[zdk j?.
d dq
(a) (b)
( )
dq dc
dc
( )
(c) (d) fJBQK ftZu'A e'Jh BjhA.
dq

16H3 ;koKP (Summary)

• wzB fbU fe CPQD teo y = f (x) B{z gqdof:s eodk j?, fiZE/ f (x), gqKs [a, b] ftZu x
dk e'Jh brksko cbB j? ns/ wzB fbU fit/A x dk wkB a s'A b sZe tXdk j? y th tXdk
jh iKdk j?. wzB fbU fe CA ns/ DB eqw nB[;ko x = a ns/ x = b T[Zs/ e'NhnK jB.
• teo T[Zs/ ;fEs e'Jh fpzd{ P (x, y) fbU ns/ wkB fbU fe PM T[;dh e'Nh j?. teo T[Zs/
P d/ B/V/ fJZe j'o fpzd{ Q (x + δx, y + δy) fbU ns/ wzB fbU fe QN fJ;dh e'Nh j?.
• nZi^eZbQ nB[ebB dk gq:'r noEPk;so ftZu s/ih Bkb tfXnk j?. fJ;B{z n;hA
fBwBfbys sZEK d[nkok ;gPN eo ;ed/ jK^
1H ;hwKs bkrs, n";s bkrs ns/ e[ZbQ bkrs
dc
( )
feT[Ai' ;hwKs bkrs & j[zdk j?, fJ; bJh
dq

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