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]