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

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

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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. 
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 + 
3. If
1 1
sin cos
,
t t
x a y a
- - = = show that
dy y
dx x
- = 
4. If y = (tan
-1
x)
2
show that (x
2
+ 1)
2
y 2 + 2x (x
2
+ 1)y 1 = 2 
5. Verify Rolle’s Theorem for the function y = x
2
+2 , [ -2 , 2] 
6. Differentiate
1
1
2
sin
1 4
x
x
+
- ? ?
? ?
+
? ?

7. Differentiate sin
2
x w.r. to e
cosx

8. If 1 1 0 x y y x + + + = prove that
( )
2
1
1
dy
dx
x
= - +

9. If cosy = x cos (a + y) prove that
( )
2
cos
sin
a y dy
dx a
+
= 
10. If x = a (cos t + t sin t) 
y = a (sin t – t cos t )
find
2
2
d y
dx
```
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