Continuity PDF

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Explain what is integration and it's continuity...

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Time :45 min 1.

CONTINUITY

Mark : 25

a) Discuss the continuity of the function 1 1 2 − x 0  x  2  1  f ( x ) = 1 ifx = 2  1 3 − x if  x  1  2 2

at x =

1 2

[Score-3]

b) Determine the value of k for the function  x 2 − 27 ifx  3  f (x ) =  x − 3 is continuity at x=3 k ifx = 3

[Score-2]

[Score-2] 2.

3.

a) Find the value of ‘a’ if the function f(x) defined by 2 x − 1 if x  2  f (x ) =  a if x = 2 is continuity at x=2 .  x + 1 if x  2    b   log(1 + 2 ax) − log 1 − 2 x    b) If the function f ( x ) =  x  K 

[Score-3]

if x  0 ifx = 0

  ( 2x )   (3x )  log 1 + a  − log 1 − b     if a) Consider the function f ( x) =   x   if Find the value of  if f(x) is continuous at x=0 . if x3 1  if 3x 5 b) Consider the function f ( x) = 7ax + 2b 9 if x5 

Find the value of a and b if f (x) is continuous of x = 3 and x =5

Bhabha Institute of Sciences Manjeri/Kozhikode/Kottakkal/Mukkam

[Score-2]

x0 x=0

[Score-2]

[Score-3]

+2/MATHS/SUB/EXAM/ 28 .09.2020

4.

5.

sin 7 x − sin x if x0  ( ) a) Consider the function f x =  tan (10x ) ( )  if x=0  Find the value of  for which f(x) is continuous at x=0 .  2x + 3 sin x if x 0  b) Consider the function f ( x) =  3x + 2 sin x  if x =0

[Score-2]

Find the value of  if f (x ) is continuous at x=0 . c) Write an example for a function which is continuous but not differentiate at x=0 .  ex − esin x if x0  a) Consider the function f ( x) =  x − tan x  if x=0 Find the value of  if f (x ) is continuous at x = 0  sin(3x ) if x0  x  if x=0 b) If f (x ) =  3  log (1 + 3 x ) if x0  x  Show that f(x) is continuous at x = 0.

Bhabha Institute of Sciences Manjeri/Kozhikode/Kottakkal/Mukkam

[Score-2] [Score-1]

[Score-2]

[Score-3]

+2/MATHS/SUB/EXAM/ 28 .09.2020...