Download GTU BE/B.Tech 2019 Winter 1st And 2nd Sem New And Spfu MTH001 Calculus Question Paper

Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Winter 1st And 2nd Sem New And Spfu MTH001 Calculus Previous Question Paper

1
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER ? I & II (SPFU) EXAMINATION ? WINTER 2019
Subject Code: MTH001 Date: 06/01/2020

Subject Name: Calculus
Time: 10:30 AM TO 01:00 PM Total Marks: 70

Instructions:
1. Attempt any five questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 (a)
Test the convergence of
3
22
1
53
( 2)( 5)
n
nn
n n n
?
?
?
??
?
.
07

(b)
Test the convergence of
2
1
.....
1 2 3 4 5 6 7 8 9
xx
? ? ?
? ? ? ? ? ?

07

Q.2 (a) Trace the curve (1 cos ), 0 r a a ? ? ? ? . 07

(b)
Sketch the region of integration and evaluate
4
10
3
2
x
y
x
e dydx
??

07

Q.3 (a)
1. If (cos ) (sin )
yx
xy ? , find
dy
dx
.
2. If
5 5 2
5 x y x ?? , find
dy
dx
.
07

(b)
Evaluate
22
R
r a r drd ? ?
??
over the upper half of the circle cos ra ? ? .
07
Q.4 (a)
Find the minimum and maximum value of
33
( , ) 3 f x y x y xy ? ? ? .
07

(b)
Evaluate
2
21
0
2
x
y
e dxdy
??
by changing order of integration.
07

Q.5 (a)
If
33
1
tan
xy
u
xy
?
?? ?
?
??
?
??
, prove that
22
2 2cos3 sin
xx xy yy
x u xyu y u u u ? ? ? .
07
(b)
Evaluate
22
2
1
11
0 0 0
xy
x
xyzdzdydx
??
?
? ? ?
.
07

Q.6 (a) Find the equation of tangent plane and normal line at the point (-2,1,-3) to the
ellipsoid
22
2
3
49
xz
y ? ? ? .
07

(b)
If () u f r ? , where
2 2 2
r x y ?? , prove that
1
( ) ( )
xx yy
u u f r f r
r
? ? ? ? ? ? .
07

Q.7 (a)
Test the convergence for
1
2
1
2 tan
1
n
n
n
? ?
?
?
?
.
07
(b)
Find the area of the region R enclosed by the parabola
2
yx ? and the line
2 yx ?? .
07

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