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# 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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