Differentiation Test - Continuity & Differentiability Class 12 Notes | EduRev

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

 Page 1


CBSE TEST PAPER-01 
CLASS - XII MATHEMATICS (Calculus : Continuity & differentiability) 
Topic:- differentiation 
1. Find the values of K so that the function f is continues at the indicated print. [4] 
cos
, x
2 2
( )   x =
2
3, if x =
2
K x
if
x
f x at
p
p
p
p
?
?
?
- ?
?
=
?
?
?
?
?
2. Differentiate the function 
sin cos
(sin )
x x
x x + [4] 
3. If
1 1
sin cos
,     
t t
x a y a
- - = = show that 
dy y
dx x
- = [4] 
4. If y = (tan
-1
x)
2 
show that (x
2
 + 1)
2
 y 2 + 2x (x
2
 + 1)y 1 = 2 [4] 
5. Verify Rolle’s Theorem for the function y = x
2
 +2 , [ -2 , 2] [4] 
6. Differentiate 
1
1
2
sin
1 4
x
x
+
- ? ?
? ?
+
? ?
[4] 
7. Differentiate sin
2
x w.r. to e
cosx
[4] 
8. If 1 1 0 x y y x + + + = prove that
( )
2
1
1
dy
dx
x
= - +
[4] 
9. If cosy = x cos (a + y) prove that
( )
2
cos
sin
a y dy
dx a
+
= [4] 
10. If x = a (cos t + t sin t) [4] 
y = a (sin t – t cos t ) 
find 
2
2
d y
dx
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