unit 1 differential calculus - IGNOU
unit 1 differential calculus - IGNOU
unit 1 differential calculus - IGNOU
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
SAQ 5<br />
SAQ 6<br />
SAQ 7<br />
SAQ 8<br />
(viii) Limit<br />
(ix) Limit<br />
=<br />
1<br />
.<br />
2 3<br />
α<br />
= .<br />
β<br />
(a) (i) Not continuous at x = 0 and continuous at all other points.<br />
(b) b = 4.<br />
(ii) Not continuous.<br />
(c) (i) 2x<br />
(a) (i)<br />
(b) (i)<br />
(ii) 6x + 5<br />
( 2<br />
−<br />
x<br />
17<br />
2<br />
− 5)<br />
2<br />
3x<br />
+ 3<br />
(ii) −<br />
3<br />
2<br />
( x<br />
+ 3x<br />
− 8)<br />
(iii) (x 2 + x + 6) cos x − (2x + 1) sin x<br />
(iv) x 2 + 1 + 2x (x + 1) – sin x<br />
− 2x<br />
2<br />
( x<br />
(ii) sec 2 x<br />
(iii)<br />
(c) (i)<br />
2<br />
− cos x<br />
2 (sin<br />
2<br />
− 6x<br />
− 10<br />
−<br />
( 1<br />
(ii) 6ax + 2b<br />
(a) Velocity = 128<br />
(b)<br />
5)<br />
2<br />
+ cos<br />
x − cos<br />
Acceleration = 64<br />
dy<br />
dx<br />
4x<br />
− 3y<br />
=<br />
3x<br />
− 8y<br />
2<br />
2<br />
x)<br />
−<br />
( 1<br />
x)<br />
( 1<br />
+ cos<br />
2 x ⎛ 2 ⎞<br />
(c) (i) x e sin x ⎜ + 1 + cot x⎟<br />
⎝ x ⎠<br />
− sin x)<br />
( − 2 cos x sin x)<br />
2<br />
x)<br />
2 3 4 ⎡ 2 3 4 ⎤<br />
(ii) ( x + 1)<br />
( x + 2)<br />
( x + 3)<br />
⎢ + + ⎥<br />
⎣ x + 1 x + 2 x + 3⎦<br />
(iii)<br />
(iv)<br />
2<br />
1 + x<br />
2<br />
1 +<br />
x<br />
2<br />
2<br />
2<br />
Differential Calculus<br />
53
Change language