5 6 )( + - = x x xf 5 6 )( + - = x x xf sin tan lim x x x

To be submitted at the respective study
centres latest by 31st December, 2014.
KRISHNA KANTA HANDIQUI STATE OPEN UNIVERSITY
Hiranya Kumar Bhuyan School of Science & Technology
Home Assignment
Bachelor of Arts (MATHEMATICS)
Differential Calculus [BMAP 02]
Third Semester, 2014
Total Marks 50
Assignments are required to be written in your own lanquage, copying in toto from
the learning material will carry less score.
1. Answer the following questions-
(2 X 4= 8)
x2 6x 5
a. Find the domain if f ( x)
f ( x)
b. Evaluate lim
xo0
x2 6x 5
tan x sin x
x3
lim
xo 0
tan x sin x
x3
c. Find the differential coefficient of the following with respect to x
x
log x a 2 x 2
d. Find the n th derivatives of y
e ax x 2 . n
y
2. Answer the following questions-
(3 X 4= 12)
dy
log 1 x ,prove that
dx
1 x2
x sin 1 x
a. If y
y
x sin 1 x
1 x2
e ax x 2 .
2
log 1 x 2 ,
sin 1 x
1 x2
dy
dx
3
2
.
sin 1 x
1 x2
3
2
.
b. Find the intervals in which the following functions are increasing or decreasing:
x 4 8 x 3 22 x 2 24 x 21
c. Find the radius of curvature at (r, 0) on the curve r=3 (1+cos T ).
r=3 (1+cos T ), (r, 0)
d. Verify Lagrange’s Mean value theorem for the functions given below.
x3 6x ,
f ( x)
1d x d 3.
3. Answer the following questions-
(5 X 2= 10)
z = z(x, y), x = eu + e-v, y = e-u – ev,
a. If
Prove that
b. If
a.
x2 y 2 z 2
U
sin 1 y
(i) If
wz w z
.
w u wQ
1
2
wz
wz
y
wx
wy
x
,
prove that Uxx + Uyy + Uzz = 0
2 log x 1 , show that
2
x 1 y n 2 (2n 1)( x 1) y n 1 n 2 4 y n
(ii) Determine y n 0 if y
y
yn 0
e m sin
e m sin
1
x
1
x
0
.
.
b. (i) Find the minimum distance from the point (2, 1, -3) to the plane 2 x y 2 z
(2, 1, -3)
2x y 2z
4.
4
x
(ii) Expand y as a Taylor series at (1,1).
yx
(1,1)
N.B. The learners will have to collect receipt after submitting the assignment with the signature
and seal of the collector of study centre and will have to keep with him/her till the declaration of
result.
……................………………………………………………………………………………………
Receipt
Received the assignment from Mr/Ms …………………………………………….Enrollment
number ………………………of 3rd semester Mathematics(Differential Calculus) BMAP-01A
(2014) on ………………2014.
Date:
Signature of collector with seal

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