Continuity and Differentiation in Mathematics, Assignments of Mathematics

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CLASS – XII SUBJECT – MATHEMATICS ASSIGNMENT NO. 3 TOPIC – CONTINUITY &

DIFFERENTIATE

1. Find the point of discontinuity for the function f(x) = 

 

 2

(^416) x

x (^) x 

2. Show that f(x) = 5x-4 a < x < 1is continuous at x = 1 4x 3 – 3x 1 < x < 2
3. For what value of K in the for continuous x = 0, f(x) (^2) 8

1 cos 4 x

 x x 
0

4. If fx f(x) = 3ax+b if x > 1 5ax – 2b if x < 1 is continuous at x = 1. find a, b 11 if x = 1
5. If f(x) is differentiable at x = a find line x 
   a,

x a

x f a a f x

6. Find values of 680 that fx given by f(x) 1 : f x < 3 ax+b 3<x< 7 if x < 5
7. If y = - cot 2 x – x by sin x , prove : dy : cot3 x 2 2 dx 2
8. If x = Cos 
   + sin , y = sin – cos, prove (^2)

2

dx

d y

sec^2 

9. If y = 2 – 3 cosx, find dy at x = 6



sin x dx

10. If y = 10g (1 + cos x), Prove d 3 y + d 2 y. dy = 0 dx^3 x dx
11. If y = tan - 2 2 2 2

2 2 2 2

a x a x

a x a x   

   show that 4 4

2 3

2 (^21) a x

a x

a dx

dy 

12. If Y = (^) x

x

e

e

1 , then show that

dx

dy

x x

x

e e

e ( 1  ) 1 ^2

13. If y = sin -1^ [ x 1  x - x 1  x^2 find

dx

dy

14 If y = Sin - 

 

 

 2 2

2 2 x y

x y = tan -1^ a, prove :

dx

dy

x

y

15. If e y^ = yx^ , prove log 1

(log )^2 

 y

y dx

dy

16. If x = a (cost + log tan t/2), y =
sin t then find at

dx

dy

t =



17. Differentiate esinx^ + (anx)x^ w.r.t. x.

18. If y = e x^ (Sin + cos x) Prove : 2 0

2

2

  y 

dx

dy

dx

d y

19. If x = 3 sin t – sin 3t, y = 3 cost - cos 3 t find (^2)

2

dx

d y

at t =

KSTSP