cbse xii hots continuity and diffentiability chapter 5

5/23/2018 Cbse Xii Hots Continuity and Diffentiability Chapter 5

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Chapter 5CONTINUITY AND DIFFENTIABILITY

1 Mark Questions

Q1Check the continuity of the function

1 , 0( )2, 0

if xf xif x

= >

Q2 Chek the ontinuit! o" the "untion ( )f x x= at # $ %

Q& Chek the ontinuit! o" the "untion2( ) sinf x x x= + at # $

Q' E#a(ine the ontinuit! o" the "untion ( )f x x=

Q5 )rite the points o" *isontinuit! o" the "untion ( ) [ ]f x x= +here [ ]x

*enotes the ,reatest inte,er "untion -ess than or e.ua- to #/

Q0)rite the points o" *isontinuit! o" the "untion ( )

2 25

5

xf x

x

=

/

Q i3e an e#a(p-e o" a "untion +hih is ontinuous 4ut not *i""erentia4-e/

Q Fin* the *eri3ati3e o" ( )2sin cos ( )x /Q6 Fin* the points in the open inter3a- 7%8 &9 +here the ,reatest inte,er

"untion ( ) [ ]f x x= is not *i""erentia4-e/Q1% )rite the *eri3ati3e o" the "untion ( ) 1tan sinf x x= +/ r/ to #/

Q11 Is it true that ( )sin sinlog cos sin log sin log cosx xx x x x x x+ = + :Q12

I" ( )x f t= an* ( )y g t= 8 then is2 2 2

2 2 2

/

/

d y d y dt

dx d x dt = :

Q1& Chek the app-ia4i-it! o" ;o--e


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Q&Fin*

dx

dy"or

2sin( )

xxy x y

y+ =

Q'I" 2 2 2x y x y++ = 8 sho+ that 2

y xdy

dx

=

Q5I"

2 21

2 2tan

x ya

x y

= + 8 sho+ that

( )

( )

1 tan

1 tan

x ady

dx y a

=

+

Q0Di""erentiate

+

xaxb

xbxa

sincos

sincostan 1

Q Di""erentiate axax aaxx +++

QDi""erentiate

11

xx

xx xx

+ + +

Q6Fin*

dx

dy"or # $

3sin

cos2

8 ! $

3cos

cos2

Q1%Fin*

dx

dy"or # $

1sin ta

8 ! $1cos t

a

Q11I" ! $ ( )

21tan x sho+ that

22 2 2

2(1 ) 2 (1 ) 2 0

d y dyx x x

dx dx+ + + =

Q12I" sin ! $ # os 7a ? !98 sho+ that

a

ya

dx

dy

cos

)(cos2 +=

Q1&I" 21 xy ? 21 yx $ 18 sho+ that

2

2

1

1

x

y

dx

dy

=

Q1'I" # sin 7a ? !9 ? sin a os 7 a ? ! 9 $ % 8 sho+ that

a

ya

dx

dy

sin

)(sin 2 +=

Q15

Chek the ontinuit! o" the "untion ( ) , 0

2, 0

x xx

f x x

x

=

=

at # $ %

0 Mark Questions

Q1I" ! $ ( )

21sin x sho+ that

22

2(1 ) 2

d y dyx x

dx dx =


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cbse xii hots continuity and diffentiability chapter 5

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