Differentiation Test- 3 - Continuity & Differentiability Class 12 Notes | EduRev

Class 12 : Differentiation Test- 3 - Continuity & Differentiability Class 12 Notes | EduRev

 Page 1


CBSE TEST PAPER-03 
CLASS - XII MATHEMATICS (Calculus: Continuity and Differentiability) 
Topic: - Differentiations 
1. Find the value of K so that function is continuous. [4] 
Kx+1    if    x
( ) at x =
cosx     if     x > 
f x
p
p
p
=
?
?
=
?
?
?
 
2. Differentiate  
2
2 cot y x = [4] 
3. Find
2
 sin cos
dy
if y xy
dx
p + = [4] 
4. Find  
x y x b
dy
if y x x a
dx
+ + = [4] 
5. Find
dy
dx
 when x = a( -sin ),   y = a(1+cos ) ? ? ? [4] 
6. If 
2 3
3 2
x x
y e e = + Prove that
2
2
5 6 0
d y dy
y
dx dx
- + = [4] 
7. If
1
cos x
a
y e
- =
 Show that 
2
2 2
2
(1 ) 0
d y dy
x x a y
dx dx
- - - = [4] 
8. If ( )
2
2 2
( ) x a y b c - + - = Prove
3
2
2
2
2
1
dy
dx
d y
dx
? ?
? ?
+
? ? ? ?
? ?
? ?
? ?
 is a constant independent of a & b. [4] 
9. Find ,
dy
dx
if 
1 1 2
sin sin 1 y x x
- - = + - [4] 
10.
(sin cos )
(sin cos )
x x
y x x
- = - Find ,
dy
dx
[4]
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