Home
Class 12
MATHS
If f(x)={(-4sinx+cosx, "for",xle-(pi)/2)...

If `f(x)={(-4sinx+cosx, "for",xle-(pi)/2),(a sin x+b,"for",-(pi)/2ltxlt(pi)/2),(cosx+2,"for",xge(pi)/2):}` is continuous, then

A

`a=-1`

B

`a=1`

C

`b=-3`

D

`b=3`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Consider the function f(x)={{:(-2sinx,"for",xle-(pi)/(2)),(Asinx+B,"for",-(pi)/(2)lexle(pi)/(2)),(cosx,"for",xge(pi)/(2)):} which is continuous at everywhere The value of B is

Consider the function f(x)={{:(-2sinx,"for",xle-(pi)/(2)),(Asinx+B,"for",-(pi)/(2)lexle(pi)/(2)),(cosx,"for",xge(pi)/(2)):} which is continuous at everywhere The value of A is

Consider the function f(x)={{:(-2sinx,if,xle-(pi)/(2)),(Asinx+B,if,-(pi)/(2)ltxlt(pi)/(2)),(cosx,if,xge(pi)/(2)):} Which is continuous everywhere. The value of B is

Consider the function f(x)={{:(-2sinx,if,xle-(pi)/(2)),(Asinx+B,if,-(pi)/(2)ltxlt(pi)/(2)),(cosx,if,xge(pi)/(2)):} Which is continuous everywhere. The value of A 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.

If f:R to R given by f(x)={(2cosx"," , "if", x le -(pi)/(2)),(a sin x+b",","if", -(pi)/(2) lt x lt (pi)/(2)),(1+cos^(2)x",","if",x ge(pi)/(2)):} is a continuous function on R, 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

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 for -pi<=x<=-(pi)/(2)a sin x+b for -(pi)/(2)

If f(x) = -4sinx+cosx for x =pi/2 is continuous then

ALLEN-TEST PAPERS-MATHEMATICS
  1. If the ratio of the coefficient of x^(10) in (1-x^(2))^(10) and term i...

    Text Solution

    |

  2. In the expansion of (5^(1//2)+7^(1//8))^(1024) if the number of integr...

    Text Solution

    |

  3. If f(x)={(-4sinx+cosx, "for",xle-(pi)/2),(a sin x+b,"for",-(pi)/2ltxlt...

    Text Solution

    |

  4. If int tan^(5)x dx=Atan^(4)x+Btan^(2)x+g(x)+C, where C is constant of ...

    Text Solution

    |

  5. Let y=(secx+tanx-1)/(tanx-secx+1).If ((dy)/(dx))(x=(pi)/4)=a+sqrt(b), ...

    Text Solution

    |

  6. Let T(n) and S(n) be the nth term and sum of first n tems of a series ...

    Text Solution

    |

  7. If alpha and beta are the roots of x^(2)+4x+6=0 and N=1/((alpha)/(beta...

    Text Solution

    |

  8. If roots of 2(x-a)(x+b)+c=0 are alpha and beta roots of (x-alpha)(x-be...

    Text Solution

    |

  9. If T(n) and t(n) be the nth term of two AP's respectively and the rati...

    Text Solution

    |

  10. Suppose a and b are integers such that x^(2)+ax+b+1=0 has positive int...

    Text Solution

    |

  11. If f'(x^(2))=(ln x)/(x^(2)) and f(1)=-1/4 then which of the following ...

    Text Solution

    |

  12. If alpha=3sin^(-1)(2/3) and beta=2cos^(-1)(1/3) then which of the foll...

    Text Solution

    |

  13. For a continuous function f(x), equation f(x)=0 has 4 distinct solutio...

    Text Solution

    |

  14. If f(x)={((sinx+cosx)^(cosecx),-(pi)/2ltxlt0),(a,x=0),((e^(1/x)+e^(2/x...

    Text Solution

    |

  15. If f(x) is a monic polynomial of degree '3' such that lim(x to 0) (1+f...

    Text Solution

    |

  16. Let there are two functions defined of f(x)="min"{|x|,|x-1|} on the...

    Text Solution

    |

  17. Let there are two functions defined of f(x)="min"{|x|,|x-1|,|x+1+] ...

    Text Solution

    |

  18. Let f(x)=(x(1-x))^(2), the sum of f(1/2019)-f(2/2019)+f(3/2019)-f(4/20...

    Text Solution

    |

  19. Lim(n to oo) (-1)^(n)sin(pisqrt(n^(2)+n)), n epsilon N is

    Text Solution

    |

  20. If f(x)=int(sinx)/(cos^(2)x)(1-3sin^(3)x)dx, then value of (f(0)-f(pi)...

    Text Solution

    |