Home
Class 12
MATHS
The value of a and b such that the funct...

The value of a and b such that the function
f(x) ` {:{(-2 sin x", "-pile x le -pi/2 ),(a sin x+b " ," -pi/2 lt x lt pi/2 ),(cos x", " pi/2 le x le pi ):}` is continuous in ` [ - pi , pi ] ` are

A

`-1,0`

B

`1,0`

C

`1,1`

D

`-1,1`

Text Solution

Verified by Experts

The correct Answer is:
d
Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF DEFINITE INTEGRALS

    MARVEL PUBLICATION|Exercise TEST YOUR GRASP|11 Videos

  • DIFFERENTIAL EQUATIONS

    MARVEL PUBLICATION|Exercise TEST YOUR GRASP|14 Videos

Similar Questions

Explore conceptually related problems

The value of a and b such that the function f(x)={(-2sinx"," , -pi le x le -(pi)/(2)),(a sinx+b",", -(pi)/(2) lt x lt (pi)/(2)),(cosx",", (pi)/(2) le x le pi ):} is continuous in [-pi,pi] are

Find the values of a and b so that the function f(x)={{:(x+asqrt2 sin x", "0 le x le pi//4),(2x cot x + b", "pi//4 le x le pi//2),(a cot 2x - b sin x", "pi//2 lt x le pi):} is continuous for 0 le x le pi .

The values of a and b so that the function f(x) = {{:(x + a sqrt(2) sin x",",0 le x lt pi//4),(2 x cot x + b",",pi//4 le x le pi//2),(a cos 2 x - b sin x",",pi//2 lt x le pi):} is continuous for x in [0, pi] , are

Find alpha and beta, so the function f (x) defined by f(x) =-2 sin x, "for" -pi le x le-pi/2 =alpha sinx+beta"for" -pi/2lt x lt pi/2 =cosx , "for" pi/2 le x le pi, is continuous on [-pi, pi].

Let f(x) = {(-2sin x, ",","if" x le -(pi)/2),(A sin x + B, ",", "if"-(pi)/2 lt x lt (pi)/2 ),(cos x, ",", "if" x ge (pi)/2 ):} Then

Let f(x) = {{:(-2 sin x,"for",-pi le x le - (pi)/(2)),(a sin x + b,"for",-(pi)/(2) lt x lt (pi)/(2)),(cos x,"for",(pi)/(2) le x le pi):} . If f is continuous on [-pi, pi) , then find the values of a and b.

If f(x)={:{(x sin x", for " 0 lt x le pi/2),(pi/2 sin (pi+x)", for " pi/2 lt x lt pi):} , then

MARVEL PUBLICATION-CONTINUITY F FUNCTIONS-MULTIPLE CHOICE QUESTIONS
  1. Let : f(x) {:(=(1-cos 4x)/(x^(2))", ... "x lt 0 ),(= a", ...

    Text Solution

    |

  2. The function (x^(3)-8)/(x^(2)-x-20) is continuous over the domain :

    Text Solution

    |

  3. The value of a and b such that the function f(x) {:{(-2 sin x", ...

    Text Solution

    |

  4. The value of lim(x to e) (log x^(2)-2)/(sqrt(x)-sqrt(e)) is

    Text Solution

    |

  5. If f(x) {:(= 4x - 3 ", for " 0 lt x le 2 ),(= 4x+ 3k " , for " ...

    Text Solution

    |

  6. If f(x) {: (=(x^(2)-2x-3)/(x-3)" , for " 0 le x le 4 ),(= (x^(2)-1)/(x...

    Text Solution

    |

  7. If the function f(x) {: (3 sin x - sin 3x)/(x^(3)), x != 0 , is co...

    Text Solution

    |

  8. If f(x) (2^(x)-1)/(1-3^(x)) , x != 0 is continuous at x = 0 then : ...

    Text Solution

    |

  9. If f(0) = 2 , and f(x) = (1-cos kx)/(x.sin x) , x != 0 , is continuo...

    Text Solution

    |

  10. If f(x) {:(=(x^(n)-2^(n))/(x-2)", if " x!=2 ),(= 1024 ", ...

    Text Solution

    |

  11. If f(x) {:((3^(x+2)-81)/(9^(x)-9^(2)) ", ... "x != 2 ),(= k....

    Text Solution

    |

  12. If f(x)= {:(2x^(2)-3", ... if " x lt2 ),(5ax ", ... i...

    Text Solution

    |

  13. If f(x) {: (=(sqrt(1+px) - sqrt(1- px))/x", if "-1/2 le x lt 0 ),(=...

    Text Solution

    |

  14. If f(x) {:(=(sin4x)/(5x)+a", if " x gt 0 ),( = 6x+4 -b...

    Text Solution

    |

  15. If f(x) =1/x for all x != 0 then : lim (x rarr 0 ) f((1-cos 5x)/x)=

    Text Solution

    |

  16. If f(x) {:(=(log (1-2x)-log(1-3x))/x", " x != 0 ),(=a", ...

    Text Solution

    |

  17. If f(x) {:(=-x^(2)", if " x le 0 ), (= 5x - 4 ", ...

    Text Solution

    |

  18. If f(x) {:( =((2^(x)-1)^(2))/(sin x.log(1+x))", if " x != 0 ),(= ...

    Text Solution

    |

  19. If f(t) = 1/(t^(2)-t-6) and t = 1/(x-2) then the values of x which ma...

    Text Solution

    |

  20. If f(x) = (1+sin x - cos x)/(1- sin x - cos x ) , x != 0 is continuo...

    Text Solution

    |