Home
Class 12
MATHS
The values of a and b so that the functi...

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

A

`a = (pi)/6, b = (pi)/12`

B

`a = -(pi)/6, b = (pi)/12`

C

`a = (pi)/6, b = -(pi)/12`

D

`a = -(pi)/6, b = -(pi)/12`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY

    TARGET PUBLICATION|Exercise Competitive Thinking|63 Videos

  • CONTINUITY

    TARGET PUBLICATION|Exercise Evaluation Test|10 Videos

  • CONTINUITY

    TARGET PUBLICATION|Exercise Evaluation Test|10 Videos

  • BINOMIAL DISTRIBUTION

    TARGET PUBLICATION|Exercise EVALUTION TEST|12 Videos

  • DEFINITE INTEGRALS

    TARGET PUBLICATION|Exercise EVALUATIO TEST|30 Videos

Similar Questions

Explore conceptually related problems

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 .

f(x)= {:{(x+asqrt2 sin x ,, 0 le x lt pi/4),( 2x cot x +b , , pi/4 le x le pi/2), (a cos 2 x - b sin x , , pi/2 lt x le pi):} continuous function AA x in [ 0,pi] " then " 5(a/b)^(2) equals ....

If f(x)={(x+a sqrt(2) sinx"," ,0 lt x lt (pi)/(4)),(2x cotx+b",",(pi)/(4) le x le (pi)/(2)),(a cos 2x-b sinx",", (pi)/(2) lt x le pi):} is continuous at x=(pi)/(4) , then a - b is equal to

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

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

If the function f(x)={(x+a^(2)sqrt(2)sinx",", 0 le x lt (pi)/(4)),(x cot x+b",",(pi)/(4) le x lt (pi)/(2)),(b sin 2x-a cos 2x",", (pi)/(2) le x le pi):} is continuous in the interval [0,pi] then the values of (a, b) are

The function f(x)=cos x, 0 le x le pi is

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.

TARGET PUBLICATION-CONTINUITY-Critical Thinking
  1. If f(x) ={(4-3x,",",0 lt x le 2),(2x-6,",",2 lt x le 3),(x+5,",",3 lt ...

    Text Solution

    |

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

    Text Solution

    |

  3. If f(y)={(((e^(2y)-1)*siny)/(y^(2)),", for "y ne 0),(4,", for "y=0):}...

    Text Solution

    |

  4. For the function f(x)={((sin^(2)ax)/(x^(2))",","where " x ne 0),(1",",...

    Text Solution

    |

  5. The points of discontinuity of tan x are

    Text Solution

    |

  6. If f(x)={:{((sin 2x)/(sqrt(1-cos 2x))", for " 0 lt x lt pi/2),((cos x)...

    Text Solution

    |

  7. If {:(f(x),=(x cos x - 3tan x)/(x^(2)+2sinx),",",x != 0),(,=1, ",",x =...

    Text Solution

    |

  8. If f(x) ={((5^(x)-e^(x))/(sin 2x),",",x != 0),(1/2(log 5+1),",",x = 0)...

    Text Solution

    |

  9. f(x)={((5^(cosx)-1)/((pi)/(2)-x)",", x ne (pi)/(2)), (log 5"," , x =(p...

    Text Solution

    |

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

    Text Solution

    |

  11. If f(x) = (tan(pi/4-x))/(cot2x), x != pi/4, is continuous in (0, pi/2)...

    Text Solution

    |

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

    Text Solution

    |

  13. The function f(x) = (x^(2)-4)/(sin x-2) is

    Text Solution

    |

  14. If f(x) is continuous on [0, 8] , where f(x)={:{(x^(2)+ax+6", for " 0...

    Text Solution

    |

  15. If f(x) is continuous in [-2,2], where f(x) = {((sinax)/(x)-2,",","f...

    Text Solution

    |

  16. The value of a and b such that the function defined by f(x) = {(7,",...

    Text Solution

    |

  17. If f(x)=(e^(x)+e^(-x)-2)/(x sin x), for x in [(-pi)/(2), (pi)/(2)]-{0}...

    Text Solution

    |

  18. Discuss the continuity of f(x)={(x^4-5x^2+4)/(|(x-1)(x-2)),x!=1,2 6,x=...

    Text Solution

    |

  19. The values of a and b so that the function f(x) = {{:(x + a sqrt(2) si...

    Text Solution

    |

  20. If the function f(x) = {(1+(sin)(pi x)/2,",","for"-oo lt x le 1),(ax+b...

    Text Solution

    |