www.vchowk.com
MIDTERM EXAMINATION
Fall 2009
MTH101- Calculus And Analytical Geometry
Question No: 1
( Marks: 1 )
- Please choose one
If f is a twice differentiable function at a stationary point
has relative …………. At
x0
f ''( x0 )  0
and
then f
x0
► Minima
► Maxima
► None of these
Question No: 2
( Marks: 1 )
- Please choose one
If f is a twice differentiable function at a stationary point
has relative …………. At
x0
f ''( x0 )  0
and
then f
x0
► Minima
► Maxima
► None of these
Question No: 3
A line
x  x0
( Marks: 1 )
- Please choose one
f
is called ------------ for the graph of a function
f ( x)  or f ( x)  
as
x approaches x0 from the right or from the left
► Horizontal asymptotes
► None of these
► Vertical asymptotes
Question No: 4 ( Marks: 1 ) - Please choose one
f ( x)  __________
f ( x)  3 x8  2 x  1
If
then
3x 7  2
►
►
►
►
24 x 7  2
3x9  2 x 2
24 x9  2 x 2
if
www.vchowk.com
Question No: 5 ( Marks: 1 )
1
dy
y

1 x
dx
If
then
►1
► -1
1
►
1  x 
- Please choose one
2
1
►
1  x 
2
Question No: 6
( Marks: 1 )
dy

dx
2 x  y  3
If
then
►2
► -2
►0
► -3
- Please choose one
Question No: 7
- Please choose one
( Marks: 1 )
dy

2
2
dx
x  y 9
If
then
x
y
►
x
y
►
y
x
►
y
x
►
Question No: 8
( Marks: 1 )
d
[sec x]  __________
dx
- Please choose one
www.vchowk.com
1
1  sin 2 x
►
 sin x
1  sin 2 x
►
1
1  sin 2 x
►
sin x
2
► 1  sin x
Question No: 9
( Marks: 1 )
- Please choose one
300 = ________

3
►

4
►

6
►

2
►
Question No: 10 ( Marks: 1 ) - Please choose one
g
Suppose that f and are differentiable functions of x then
d
[ f ][ g ] 
dx
www.vchowk.com
[ f ][ g ]  [ f ][ g ]
g2
►
[ f ][ g ]
►
►
►
[ f ][ g ]  [ f ][ g ]
[ f ][ g ]  [ f ][ g ] -correct
Question No: 11 ( Marks: 1 ) - Please choose one
g
Suppose that f and
are differentiable functions of x then
d f

dx  g 
[ g ][ f ]  [ f ][ g ]
g2
[ g ][ f ]  [ f ][ g ]
g2
►
►
[ g ][ f ]  [ f ][ g ]
f2
►
[ g ][ f ]  [ f ][ g ]
f2
►
Question No: 12
( Marks: 1 )
- Please choose one
If a function g is differentiable at a point x and a function f is differentiable at a point
g(x), then the ________ is differentiable at point x .
► Composition
(f o g)
► Quotient
(f/g)
► Product
(f . g)
► Sum
Question No: 13
(f + g)
( Marks: 1 )
- Please choose one
Chain rule is a rule for differentiating ___________ of functions.
► Product
► Sum
www.vchowk.com
► Difference
► Composition
Question No: 14
( Marks: 1 )
-correct
- Please choose one
d n
[ x ]  nx n 1
dx
The power rule,
holds if n is __________
► An integer
► A rational number
► An irrational number
► All of the above
Question No: 15 ( Marks: 1 ) - Please choose one
Let a function f be defined on an interval, and let x1 and x2 denote points in that
f ( x1 )  f ( x2 )
x1  x2
interval. If
whenever
then which of the following statement is
correct?
► f is an increasing function.
► f is a decreasing function.
► f is a constant function.
Question No: 16 ( Marks: 1 ) - Please choose one
Let a function f be defined on an interval, and let x1 and x2 denote points in
f ( x1 )  f ( x2 )
x1  x2
that interval. If
whenever
then which of the following
statement is correct?
► f is an increasing function.
► f is a decreasing function.
► f is a constant function.
Question No: 17 ( Marks: 1 ) - Please choose one
f ( x)  0
If
on an open interval (a,b), then which of the following statement is correct?
► f is concave up on (a, b) -correct
► f is concave down on (a, b).
► f is linear on (a, b).
Question No: 18
If x  0 then
( Marks: 1 )
- Please choose one
d
[ln x]  ___________
dx
www.vchowk.com
►1
► x
1
► x
ln
►
1
x
Question No: 19
( Marks: 1 )
y  ( x  2 x)
3
Let
- Please choose one
37
. Which of the following is correct?
dy
 (37)( x3  2 x)36
dx
►
dy
 111x 2 ( x3  2 x)36
dx
►
dy
 (111x 2  74)( x3  2 x)36
dx
►
dy
 (111x 2  74)( x3  2 x)38
dx
►
Question No: 20
( Marks: 1 ) - Please choose one
What is the base of natural logarithm?
► 2.71
► 10
►5
► Any real number
Question No: 21
( Marks: 1 ) - Please choose one
dy
 __________
dx
x2  y 2  1
If we have
then
www.vchowk.com
x
y
►
x
y
►
y
x
►
► None of these
Question No: 22
( Marks: 1 )
- Please choose one
logb a r  ________
►
a log b r
►
r log b a -correct
log b a
log b r
►
►
log b a  log b r
Question No: 23
log b
( Marks: 1 )
1
 ________
c
►
►
►
►
log b c
1  logb c
 log b c
1  logb c
- Please choose one
www.vchowk.com
Question No: 24
log b
( Marks: 1 )
- Please choose one
1
 ________
t
►
►
►
log b t
1  log b t
1  log b t
►  log b t
Question No: 25
Differentiate:
-correct
( Marks: 3 )
yx
x
e 5 x 6
Question No: 26 ( Marks: 5 )
y  ( x3  7 x  1) (5x  2)
Differentiate
Question No: 27 ( Marks: 10 )
The derivative of a continuous function is given .Find all critical points and
determine whether a relative maximum, relative minimum or neither occur there
f /  x   2Sin3 x  Sin2 x
; 0  x  2