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# Indian School of Mines 2010-1st Year B.Tech Petroleum Engineering F semester - Question Paper

Wednesday, 23 January 2013 03:45Web

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\o + ibJ

- (?)

(7)

a-b

QQ2,,3how that sina + xsin(ar + /?) + -sin(ar +2/?)+.......... = exme sip(a + xsin /?).

DEPARTMENT OF APPLIED MATHEMATICS

Mid Sem. Special Exam for I-Sem. B. Tech (Common)

Session: 2009-10 Subject: Mathematics-I (90 Marks)

Course No: AMC 11101, Time: 2 hour*

Instructions: Use separate answer book for each pan.

All questions are compulsory.

Figures in the margin indicate full marks.

PART-I (Calculus I: 30 marks)

Q1. Expand = sin(/r sin"1 x) in infinite series in powers of x.

Q2.Use Jacobians to show that u = *-+ - , v = tan'1 x - tan1 y are not dependent and find

1 -xy

relation between them.

Q3. Find rih derivative oflog(ar + x2).

j,,,     , . , 1 6 f , 56 cd

(X'lf 6 = tne" , find value of n forwhich j r = .

J'. '    r~ cr \ cr) Or

PART-II (Calculus II: 30 marks)

oq |    ~'2

Ql. Test for convergence of (i) f=-dx (ii) f-dx.

\x-!+l    J0 x

r t x

Q2AJsing the technique of differentiation under inteera! sign evaluate j cot'1 (r)d.~.    (S)

\vy     a

t Q3-. Discuss the convergence of (1 - x)~'dx.    d)

o

4nyn

Q4. Show that /?(, ri) = ===== .    w)

iy)n + U2

Part-Ill (Trigonometry & Algebra: 30 Marks) lab

.'Qli Prove that tan

v y

111 1

(<Q'Prove that the infinite series + + +    +.......=c is convergent if p > ! and divergent if

-    I' 2n y n

p< 1. (8) _Q4. Test the convergence of the following series    (4+4)

/f7 1 3 5

0\li) -+-+-+.......CO

't&S 1.2.3 2.3.4 3.4.5

X1 AT3    - - -

(ii)x+y+y +.......OO    /''J

1 c ,j' i' J 