Kurukshetra University 2008 B.A Mathematics Calculus - Question Paper

Roll No.    Ttn.il 3    3.

32

BAE/A08 MATHEMATICS (Calculus) Paper - BM-102

16a

9 '

lb) Tracc the curve

r = i<I - sin 0)

SKCIION-II

() Pt.nc that */:

J \n²*A dx

P?+P:

fU.A. : 30 B.Sc.: 45

(Maximum Mark* :

2;i!

I.

i <4tt) J (4H)

6.

vaxis.

I. (a) If /(> x^r + - 3* 11, find llie value til

/( Yq ) *tlh ihe help of Taylor'* wiled loi Jt.\ f hy

S <4W)

a

<b) Prove lliat the curve * |__cosq Im Ho asymptotes.

3 <4Vi)

Note : Attemptquestions in all. velecting m least one quc'tion from eKh section. Marks for B.Sc. arc given in brackets.

SECTION-1 (a) lf/(*) it differentiable ai x a. find

(b) State and prove Leibnitz'* iltcorcm.

Time : Three Hours]

.t-n

Li

(2"t,.>!)-' 2 ^{3 4W}> (h) hind the length of the arc ot ihe par.tl'oh .r = 4v

(i)    from the vertex to an extremity nl the Inti is rcctum

(ii)    cut-off by lams rcctum.    3 <4Vi)

(a)    Find the intrinsic equation of the r<irdioid

r = ai\ - cos 0).    3 (4Vi)

(b)    Find the area common to the par. >ln-

v² 4<u and .r³ = 4<jv.    3 (4 Vt)

(a) I^;iikI the volume of ihe solid obtained by icvolving the i-ardioid r = (l + cos 0) about (he initial liiv.    3 (4Vi)

(h) l^;md the .surface of (lie solid generated by revolving

(a) If p,. _p₇ be the radii of curvature ai the extremities of any chord through the pole of the cardioid r a{\- cos 6). show that 2

3 (4V4)

the loop of the curve x = tK y a / - about

3 (AVt)

3 <4W)

R

32/8.000/KD/5y

(P.T.O

rf^Jv .dy . ₂

TT ^{+ 2v x e}    3 <4W)

dx dx

d*x

"d?

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