MTH101 Current Finalterm papers

by laila Mon Feb 06, 2012 12:43 pm

MTH101 Latest Paper 3-02-2012
Total 52
40 mcqs
12 short questions
41. Find a definite integral indicating the area bounded by the curves
y = x − 7
and
2 y = x
between
x = 0 and x =1
. But do not evaluate the integral.
2 marks
42. Evaluate the improper integral
2
3 2
dx
x
+¥
_
2 marks
43. Only write down the Maclaurin series for
C os(x)
.
2 marks
44. Evaluate:
4 3 2
1
6 5 4 3 2
lim
x 1
x x x x
®− x
− + − +
−
2 marks
45. Show that
lim 0 k
k
a
® +¥
=
for the following alternating series
( ) 1
2
1
1
1
k
k
k
k
+
¥
=
−
+
_
3 marks
46. Evaluate the integral:
3
1
( 1)
x
_ t + dt
3 marks
47. Find the work done by the force 400x if an object moves in the positive
direction over the interval
[0.15,0.18]
?
3 marks
48. Find equation of the line having slope 3 and passing through the origin.
3 marks
49. Evaluate the integral:
2
1
.(1 )
dx
x + x
_
by using a proper substitution.
5 marks
50. Evaluate the improper integral
5 marks
51. Show that
1
n a
¥_
is divergent for the following alternating series.
1
1
( 1) . !
2
n
n
¥ − n − _
5 marks
52. Find the instantaneous rate of change of
3
0 f (x) = x +1 at x
5 marks