Indian School of Mines 2010-1st Year B.Tech Petroleum Engineering F semester - Question Paper
IT)
,421
\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
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Attachment: |
| Earning: Approval pending. |
