Differentiation Test- 4 - Continuity & Differentiability

# Differentiation Test- 4 - Continuity & Differentiability - Class 12

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CBSE TEST PAPER-04
CLASS - XII MATHEMATICS (Calculus: Continuity and Differentiability)
Topic: - Differentiation
1. Discuss the continuity of the function [4]
-2,      if        x -1
( ) 2x,     if       -1 < x 1
2,       if        x > 1
f x
=
?
?
= =
?
?
?
2. Find
dy
dx
if
sin( )

cos( )
ax b
y
cx d
+
=
+
[4]
3. Find
dy
dx
if
3
1
2
3
tan
1 3
x x
y
x
- ? ? - =
? ?
- ? ?
[4]
4. Find
dy
dx
, if y=
1
( cos ) ( sin )
x
x
x x x x + [4]
5. cos log tan
2
t
x a t
? ?
= +
? ?
? ?
, sin y a t = find
dy
dx
[4]
6. If ( 1) 1
y
e x + = show that
2
2
2
d y dy
dx dx
? ?
=
? ?
? ?
[4]
7.
2

2
a
t
t
t
y a and x t
+
? ?
= = +
? ?
? ?
Find
dy
dx
[4]
8.
1
1 sin 1 sin
cot
1 sin 1 sin
x x
y
x x
- ? ?
+ + - =
? ?
+ - - ? ?
[4]
9. If cos cos cos ........ y x x x = + + + Prove that (1 2 ) sin
dy
y x
dx
- = [4]
10. log tan
4 2
x
y
p
? ?
= +
? ?
? ?
Show that sec 0
dy
x
dx
- = [4]
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